That sounds functional in the sense it would work, but it would require you to essentially run a library full of 25 nuyen books, one for each unique aura found, which would take an eternity to set up. On top of that you don't record signatures, you record full auras so it would probably take people a few tries to read it. It would require full time staff to maintain, and space to store it, and because its based on physical records there would be massive latency as you shiped mages across Seattle (remember, its fucking big and each 'district' is basically a full blown city) so we are talking a lot of nuyen, time, and labor to....
Do what exactly? How does this help the corp bottom line? While this is an interesting hypothetical system to allow the relaying of the information on auras, it isn't efficient either way and it doesn't... actually help the corps practically speaking.
Remember, they don't really give a fuck about catching shadowrunners, and even if they did, how does knowing the same aura was at a few different corp sites help them 'make your next run more sketchy?' Like what are they going to do? Have every security mage take a day trip down to the KE Magical Aura Library in Tacoma and all crowd around a single mana plate trying their best to assense it? How often do you force mages to re-evaluate the, again, literal library of auras, which probably is a multi-day task?
Real world, Washington has a crime rate of 3 per thousand, but Seattle itself has a crime rate of 60 per thousand, or around 20 more times due to more crimes being commited in urban areas. In SR, it is officially a felony rate of 12 per thousand. Lets just assume we only look at Felony magical charges.
Demographics information in SR sucks complete ass, because the writers lack a sense of scale and generally 'under-assume' population percentages. However, in SR, Seattle has a population of 4,000,000. This means that, yearly, 64,000 people are the victims of felony crimes. Lets pretend every crime is done by one individual and ignore the fact that in most criminal scenarios we would be talking about mage-gangs with multiple perpetrator auras: One crime is one aura. Maybe the magical photographers are really good at capturing all their auras in one frame.
In SR, 1 in 100 people are magical, lets assume that despite magical talent tends to lead to recruitment into gangs and syndicates that it is completely balanced out by corporate recruiting (its explicitly not and its a plot point that the resentment people feel towards mages having a 'golden ticket' is unfair, but lets pretend it is because honestly I don't like 'poor little mage' plots myself). This means that, in Seattle, there are 6,400 astral plates taken a year.
Assuming a mage could analyze the aura correctly first try, every time, and worked 8 hours a day going through them, and it took them 17 seconds to store and retrieve another plate (maybe they have assistance from a plate-librarian helping us get to the nice even number of 20 seconds per-plate, or 3 plates a minute), they could get through a year's worth of plate content in a solid week's work.
So, one mage, working 8 hours a day, can catch up on the year's worth of plates. To learn the auras of, mostly, random go gangers and mages running shadowruns, to do... what with this information? How does this help them stop shadowrunners? You see a spell with an unfamiliar aura anyway and you probably are already sounding the alarm. How does knowing 'oh this person hit some random corp ages ago' help?
This system gets worse and more nonsensical when you look at how many police there are in Seattle. In 'dense' cities like NY or in Sprawls like LA, you get around 40 police per 10,000 people. This is low for SR, but lets run with it anyway. That means .4% of Seattle are law enforcement officers, or 16,000 officers. Lets, again, pretend its 1 in 100 are mages and all of them can do this assensing that well. We know that more than that are mages, and no most probably can't hit the net hits to read a signature from an aura consistently enough to do it in a single turn, but lets pretend. That is 160 mages on the force each spending around 4 and a half days to read the year's felony auras.
That means that payroll is billing 5,760 mage-hours (which are more expensive than regular man-hours) at least to ensuring every mage on the force is learning some bullshit auras that, again, practically speaking, do nothing but let the assenser recognize the aura. But it gets worse because, unlike auras, you DO need to make memory tests to remember case names, so you can't even pretend the mages are actually remembering all these auras to corelate them because what wagemage is going to remember 5,760 case names and what auras they relate too? Also, those 5,760 plates cost over 100,000 nuyen. In SR, a very high quality executive protection suite for a year costs about that much (according to Vice). Is a catologue of random wizgangers and shadowrunners really worth as much as protecting the life of your CEO?
This hypothetical library works better as a detective's resource to corelate cases, but even then, such a scattershot technique doesn't make sense. Your spending a week to go through a year's worth of cases, and if someone's been operating for longer you need to do more. Obviously you get more benefit from corelating cases and then storing them together, but that level of efficiency requires us to remember that crimes can contain more than one person and will have mages more often than the normal population and suddenly the plate number balloons out.
And, again, what is the actual endgame here? "Oh great, we discovered that the shadowrunner with aura 27RZJB22's runs target random corporations with no rhyme or reason, almost as if their motivation was purely mercenary. This will surely help us crack the case and catch them, despite the fact we explicitly don't care about catching them and its literally one of the first things the setting establishes.'
The assumption that astral signatures are a big deal falls into the same trap of assuming DNA evidence or fingerprints matter, or the trap that some Gms have of trying to figure out how KE would bust the runners. It misses the fundamental point of the setting to try to come up with these clever ways to get data on the runners and put the screws too em for having the audacity to run: The setting is about totally anonymous crime. A huge part of the concept of SR is that our authority figures have no actual interest in keeping us safe and instead just want to hold onto power and maintain a status quo as best they can, and they will cut any corner they can (including actually stopping criminals) to obtain more wealth. KE and Lonestar in the setting are not 'protect and serve' agencies, they are a for profit company, and KE is literally owned by Ares, who is selling gear to runners and wants runners to exist and blow shit up because that helps their security contracts, which is why KE and Ares Johnsons are explicitly super open and chummy to runners. Like the cops in shadowrun are friends with shadowrunners. They aren't hunting you like dogs. Part of why Shadowrunners often go on 'investigation runs' as borderline PIs, and why so many PIs are also runners, is in part because the police sincerely do not care about catching criminals in SR, and often the only way to actually solve a crime is to hire someone who's job is to solve that specific crime, and not to maintain close rate quotas and cheat doing it by nabbing random powerless SINless to avoid sending HTR teams after scary powerful SINless who make a living defying HTR and destroying corporate profits.
Almost any question that can be summarized as 'how can I use X to bust some runners after the fact, rather than try to deter losses on the run itself' can and should be answered by 'you don't. That is explicitly not how the setting works, even though many runners are political the underlying assumption that runners are deniable assets exists to prevent GMs from turning the game into reverse CSI.'