The loudspeaker enclosure has a pronounced effect on the sound of the speaker system; it is not just there to hold the
speaker drivers in place.
So what does the enclosure do?
Imagine this experiment... Obtain a fairly large, sealed box 3-way loudspeaker system. Obtain a few tools (an arc welder, an anvil... all the usual stuff). Take this lot home. Remove the drivers from their enclosure, and then mount them with a minimal enclosure - like by bolting them to a rigid steel skeleton. Very avant garde! I would love to have skeletal speakers in my house! But what happens to the sound?
The output from the tweeter and from the midrange may be improved in some ways, a little more clear and 'fast' sounding. However, the tonal balance will be altered a little, the lower end of the midrange reduced in level. Also, the power handling of the midrange will be lower, with some extra distortion at high sound levels.
The woofer will suffer a lot. It may, like the midrange, sound a little more clear and 'fast', but it's output will be vastly diminished. This will ruin the sound balance of the system. Also, power handling will be hugely reduced, and distortion at high sound levels will be massive - and the driver would be more vulnerable to damage.
Why does the woofer suffer so much?
Tonal balance:
The walls of the box prevent the back wave of the driver from interacting (mostly destructively) with the front wave. It is this destructive interference which kills the bass output when the driver is not enclosed. Controlling the back wave of the driver (by whatever means) is necessary for a good sound balance. DIfferent enclosure types do it different ways - sealed boxes just eat it up, whilst most other types let some of the back wave out to play.
Damage and distortion: when the woofer is set into an enclosure, the sealed box traps a volume of air behind it. As the driver moves, it has to squish or strecth the air in the enclosure to do so. This mass of air resists being messed with, and also acts like a spring, attempting to return to it's original volume - and does so more strongly in proportion to how compressed / rarefacted it is. This spring-like effect helps to prevent over-excursion of the driver, and can reduce both distortion and the likelyhood of damage to the driver.
Actually, that's pretty much it - the enclosure just convinces the air behind the driver to behave differently to the air in front :)