It's been that way since season 1--the 1 top 1 jungle 1 mid 2 bot (1 carry 1 support). It's for various reasons.
Each lane has only one person taking creeps for the optimal distribution of gold. If a lane is empty, there's a ton of gold, EXP, and pressure being thrown away for nothing. So we put one person in each lane to farm creeps, base. That leaves us with two players. One goes to the jungle for, again, optimal distribution of gold, and to not waste that wealth of gold, EXP, and pressure. That leaves us with one player, who has become a 'support', which I'll get into in a bit.
Why do we have the types of champs we do in each lane?
Top is a long lane, so the champs that play there have to have to ability to survive a gank or a chase down that longer lane. This can mean having a certain amount of mobility, tankiness, or a combination. There are exceptions, but those are riskier. You don't want a support with those toplane champs because there's not really a reason to support them. Compared to supporting an ADC, you just don't get much out of it
Junglers have a few options nowadays. They can be scaling carries (Fiddle, Kha, Shyv), tanks (Sej, Nunu, Mundo), champs with early gank pressure (Lee, Elise, Eve), etc. The only prerequisite is that they can survive against and kill the jungle creeps alone early on, since the point of having a jungler is to take the gold and experience efficiently from it, which is why you don't see shit like jungle Jinx or Anivia. Why not have the support help the jungler clear camps? It would either delay their scaling, or delay their level 2/3 powerspike for their early gank. And if the support just didn't take any gold or experience, you'll have an incredibly starved player who gets blown up instantly by anyone on the other team come midgame when they have no items completed and are 4 levels down.
Mid is a short lane, allowing for squishier/less mobile picks, which tend to have high midgame and/or lategame damage. Mid lane champions are the carry champions the vast majority of the time, carrying their team through their particular strengths--waveclear, high single target burst damage, high aoe damage, high poke damage, etc. Those champions go midlane because midlane is the place where you can maximize a single player's gold income. Along with that lane's creeps, there are multiple nearby jungle camps (raptors, wolves, blue), and the midlaner is able to roam effectively to two other lanes, where bot and top can only effectively roam to one (with the obvious exception of the occasional TP gank bot from top). You don't want a support mid because it would take away from the midlaner, mostly in the form of experience, when this is supposed to be the player for your team come midgame. And to take your situation, with the support holding the lane while the mid roams--it would just be better all the time to have the support roam with the mid. There's no reason to make it a 2v1 when you could make it a 3v1. And, when the enemy mid follows the roam, there's nothing stopping their support from accompanying their mid, making the 2v1 in your favor become a 2v3 in the enemy team's favor.
Bot is what we have decided to make the 2 person lane. Why? Why not have the ADC+Support top and the second solo laner bot? It's pretty simple, actually--dragon pressure. Having more members in the bottom lane makes contesting dragon easier. If you have 4 people near dragon (mid+jung+adc+support) and the enemy team has only 3, your team has a huge advantage and will begin snowballing an objective lead from the second the first dragon is taken. And then there's as for why have those two members be an ADC and a support. ADCs, without a support, would have to go mid, because they don't have the tools discussed earlier to survive in a long lane. They're (usually) both squishy and immobile. That would shaft the champs currently playing midlane into a long sidelane, where less gold income and roaming opportunities are present. But, with the aid of a support, an ADC can survive in a long lane and safely get the gold they need to scale into lategame carries that can quickly kill the enemy team's towers, inhibs, and eventually nexus.
TL;DR supports don't go jungle because they'd be heinously underpowered and the jungler would get hurt just about as much as they'd get helped, especially with the new changes to how EXP works in the jungle. They don't go mid because the midlaner would get shafted from the EXP that they need midgame. They don't go top because the toplaners don't really need it. ADC+Support go bot because dragon pressure, supports support an ADC bot to make sure they survive the long lane and to help their transition into lategame.