This got explained earlier in the thread but in different words, so here goes:
A driver's diameter is only one stat that determines its performance. Another big one is its Xmax, or, roughly, how far the surface (usually a cone) can move back and forth in a controlled manner. Xmax (the distance the cone can move) times Sd (the surface area of the cone) gives you the volume of air the driver can push around, and you need to move a lot of air if you want to generate SPL at low frequencies. To work well at low frequencies the speaker generally also needs to be built with lower resonant frequency (which usually means heavier and stiffer). To move that bigger, heavier stiffer cone you need a much stronger motor, which will naturally be less efficient. The whole thing will tend to have a natural rolloff at a lower frequency than a conventional woofer, and even if that isn't an issue, the general construction optimized for LF tends to result in breakup and other nastiness fairly low in the frequency band.
You can see this in these examples of 5 1/4" driver:
View attachment 235309View attachment 235308
The woofer driver is built to supply
some bass. so it has a reasonably flexible surround, etc, but it also has features to help it control output up to where it can cross with a tweeter. The subwoofer driver has a much more exaggerated surround, spider (not visible) and greatly enlarged motor.
Alternately, adding surface area to the low-frequency driver of a speaker boosts efficiency. (It's easy to make higher-frequency drivers more efficient so the LF driver tends to determine total speaker efficiency.) But then optimizing it for lower frequencies lowers that efficiency back down. So dialing for these two factors becomes a big part of the speaker design. You can have speakers with large (12-15") woofers without much LF extension at all, because they're optimized way on the efficiency side.
This is what the posters earlier talking about Thiele-Small parameters were getting at. So within the bounds of Hoffman's Iron Law, you shouldn't assume that 'small driver' = 'little bass' or that 'big driver' = 'lots of bass'
That doesn't get into cabinet construction either, just because a speaker is large doesn't mean it's particularly tuned to put out a lot of LF, and a full-range speaker does have to dedicated internal volume to other stuff.