BJTs tended to be cheaper than MOSFETs for the same power handling, or going back far enough, MOSFETs of adequate ratings weren't available at all. In a typical SMPS application, the question breaks down to this: is it cheaper to use a drive transformer (which, thanks to feedback, neatly solves the base drive problem), or MOSFETs with some kind of driver? Also, before bootstrap gate drivers came on the market*, you'd just be using a gate drive transformer anyway, so what's the point?
*And this required a process advancement. These aren't simple ICs: the high side logic is on the same substrate as everything else, and none of the standard logic (high or low side) handles more than, whatever, 8, 18, 30V -- yet it's able to fly at 600V or more above it! They use a deep well diffusion, or epitaxy or something, I forget exactly what -- to provide this isolation capability, and the high side logic is simply built on top of it. Very much a custom process step, fabs had to dial it in. Big investment. So they weren't feasible until the applications were there -- i.e. the resulting product, combined with ever-cheaper and more powerful MOSFETs, was cheaper than a drive transformer with BJTs or MOSFETs.
For stuff like motor and solenoid drivers, you had your standard 30-40V bipolar fab, which made good NPNs and shit PNPs (lateral), or somewhat later (70s?) actual complementary bipolar came along, at added cost of course (more process steps). So you had your LM317s and L298s and so on, mostly Darlington outputs, modest switching speeds (1us to fractional us), lots of loss but it's still nowhere near as inefficient as a linear amp, or a ballast resistor for solenoids and steppers. You make up for the conduction losses a little bit by using higher supply voltages, L298 is fine at 24V supply for example. Sure beats the pain of wiring everything from discretes.
Later, Sziklai outputs, just plain saturated NPN/PNP switches, and controlled-saturation switches came along, which I don't know any examples offhand**; and later still, integrated CMOS which are still in common use today.
**LM1117 is kind of an example, but I forget if its PNP pullup is still lateral and just a big fucker, or if it's complementary process.
LT (now ADI) likes (liked?) to make a lot of bipolar circuits, with quite good performance, in part thanks to their captive fab. Switching regs with 2-30V input range, and a bootstrapped output (buck type), are a typical example. Yes, they bootstrap an NPN -- you need relatively large bootstrap capacitance, and it's fed from a low voltage internal supply (2-5V say) since it doesn't need much voltage. That's in part how it starts up at such a low voltage, and it's not particularly derated down there either (whereas CMOS you might expect is running out of poop, say at 3 or 4V, if it starts or runs at 5-8V nominally). They got switching performance comparable to anything else on the market. Presumably with fairly complicated drive circuitry: controlled saturation, boosted turn-on and turn-off edges, level shifting, etc. And just a well tuned output transistor structure, lots of emitter and base connections so it turns on and off quickly, I would assume. Which is perfectly reasonable with fabs today, you can fit a lot of 200nm transistors on a die -- not like the old days where you're hard pressed to fit more than a few hundred 10um transistors on the thing.
Tim