As if this needs explaining and pro's can explain this sooo much better in fact JaK you can explain this so much better but alas here we go.
MSC was initially tied to each individual Nexi and you could only have 1 of them. The intention being that Photon Overcharge would help deal with drops and Mutalisks since both Medivac speed boost and Mutalisks base speed as well as Mutalisk regeneration going into HOTS was buffed, Protoss on the other hand didn't get any actual units that could deal with these new additions to the other races. It also helps Protoss to secure and hold bases against early pressure since Protoss unlocks there AOE and ability to crush on the battlefield later in the game with Colossus, HT, Disrupter, Archons, Upgrades etc.
Terran and Zerg got better tools to harass with in HOTS and Protoss got a defensive ability instead of a battlefield unit to help deal with this new threat which helps to cement Protoss as a defensive race until critical mass is attained. This defensiveness has tried to be mitigated through the use and the stat upgrades of the Warp Prism and to its credit, it has given Protoss a viable harassment option in the Mid as well as the Late Game. However if you take the WP out of the equation for a moment how is Protoss harassing a Zerg or Terran in the early or mid game other than going phoenix/oracle? The answer which I will touch on later is they aren't and for a very good reason.
This bleeds into the second ability in the MSC, that being the Mass Recall, this meant that Protoss ground armies could move out earlier in the game and in the mid game and harass/ stop droning to pressure their opponents with two outcomes. 1) providing necessary harassment that Protoss needs to do in order to stay on a level playing field/ get ahead of their opponents and 2) to allow Protoss to attack/pressure before attaining critical mass (something previously they were nervous (to say the least about doing )).
Finally, Timewarp. This allows Protoss to dictate how an engagement occurs by forcing the opponent to either engage or retreat instantly. And If timewarp lands atop your army suddenly the combination of Timewarp+Forcefield+Guardian Shield+Protoss army means that, that group of units is dead since it is slowed, has their attack damage reduced, is unable to retreat and is separated from the rest of the army. Timewarp acts like a soft ForceField meaning that armies are not going to Want to move into that area as they are at an immediate disadvantage. There is little to no counterplay for the army opposing timewarp to do other than run, don't enter it or die.
The MSC is the bandaid to end all bandaids. Let's say for example the MSC is removed from HOTS (just for the sake of argument) tomorrow. Suddenly those glaring issues that the MSC attempts to cover up are exposed and Protoss 1) cannot hold 3 Base vs 3 Base or 3 Base vs 4. 2) They die eventually to Speed medivac drops since Photon overcharge can no longer let them be in two places at once without actually committing their army (or a large portion of it) 3) Mutalisks ravage every Protoss from here to kingdom come, thus going anything but Stargate or Blink would immediately become impossible since the 2/3 base Mutalisk Zergling strategy into a hydra tech switch would become impossible to deal with without losing a critical number of units. 4) Protoss vs Protoss goes back to the horrific scene it was in Wings of Liberty and I guarantee that no Protoss player wants that. 5) The underlying issues of Protoss design would finally be exposed which is that Protoss does not have the strength in its ground forces that it needs to compete with those of Zerg or Terran.
Protoss ground units however need to be weak in the current HOTS and LOTV build of the game otherwise Force Field and Warpgate attacks would become unstopppable.
I know everyone as well as Blizzard must be sick to death of hearing this but those two mechanics need changes. I would recommend moving warpgate up to Twilight council tech, making its cooldown as long if not a little longer than the total time it takes a gateway to build a unit in standard time and buffing all Protoss ground units to compensate, thus turning WG from a necessity to a CHOICE which can aid you when initially attacking the enemy however the longer you use it for the greater a disadvantage you place yourself at. I'm tired of talking about what is to be done with FF, I as well as many other wouldn't be sad to see it and that is my suggestion for it, alongside the aforementioned changes suggested though, not separately or another combination of changes.
Great suggestions have been mentioned in this very subreddit as well as on the Blizzard forums. If Protoss is to exist in a world without the MSC or where they no longer need to rely on Spells and/or bandaids to patch up their glaring weaknesses then changes to other fundamental mechanics of Protoss need to change as well.
Tl;dr The MSC is a bandaid, its sits atop things like Warp Gate and Force Field as well as weak Protoss ground units. If MSC is to be changed or removed these mechanics need to change as well.
PS. Mothershipcore is not at all fun, it creates infuriating scenarios for players and acts as a bandaid for other Protoss related issues.