I guess the first thing to note is that the postwar APC and IFV are a development of the half-tracks used in WW2, not a completely new idea. They also share some similarities with infantry riding on tanks - though they're usually a lot safer for the infantry.

I know a little bit about postwar Soviet doctrine, although I can tell you exactly how it changed compared with WW2 doctrine.

In Soviet doctrine the BMP (and I think also BTR) is integral to the infantry squad, to the extent that the squad leader is actually tank commander. A soft-skinned vehicle obviously can't keep the same close contact with a squad that an armoured one can.

The doctrine is about maintaining the pace and momentum of attack. This is much much easier if you don't have to keep calling in dismounting and re-mounting and calling in soft-skinned transports from safe areas. I've read a report of a proper military wargame where the Soviet side advanced an entire battalion through a town along a single road which happened to be undefended. That kind of rapid and bold exploit relies on integrating your infantry and their transports. It's no good if one guy can appear with a machine gun and hold up your whole column.

Here's my friend's description of how a Soviet mechanised attack was meant to go:

"A Soviet Motor rifle company would be mounted in BMP's with 4 attached tanks, two with the lead platoon, and two with the remaining platoons. These would lead the assault (in open ground at least - closed ground reverses this somewhat).

The attack would be preceded by a massive bombardment aimed at taking out known or suspected AT postions.

The entire company would form up in line, about 1,500m from the enemy. BMP's 50-100m apart, tanks more widely spaced.

The line rumbles forward to 300m, where the infantry dismount to attack. They move as fast as possible, but go to ground if not.

Advances are done on a company-by-company level, so the entire company stops and goes to ground, or get moving.

Clearly, if you're disembarking infantry at 300m, then that's inside small arms range, which means you need highly suppressive weapons, as the BMP and BTR have. The tanks were the main leaders of the assault, so it was important to have the best MBT's they could, but also have them cheap enough to mass-produce. Even T-72's with ERA are/were surprisingly good in testing, apparently."

So this doctrine relies on having APCs that are able to withstand small-arms fire, and vehicles that are able to suppressive fire (which might as well be the APCs - hence IFVs are developed).

A further consideration is that Soviet doctrine is tied up with a battlefield where nuclear, biological or chemical weapons have been used. This means that if at all possible you want to stay in your safely enclosed vehicles. So the BMP is built as something troops can fight from, and that they can shelter in unless they really have to leave.