Let's face it, they do sound bad. If you haven't realized that, then you either haven't been listening or you think that they are supposed to sound that way.
Compare a small PA loudspeaker cabinet against a good hifi loudspeaker, at a level the hifi loudspeaker can stand of course, and you will soon be in no doubt whatsoever.
But there have to be reasons why small PA loudspeakers sound bad. After all, decent hifi speakers can sound really good, and a large PA (providing that it isn't made up of multiple small cabinets) can give hifi speakers a run for their money.
Going back a few years, there once wasn't even such a thing as a small PA loudspeaker. No-one had thought to try. But the the oddball Bose company came along with their model 802 small full-range cabinet.
The great thing about the 802 was of course that it was small and easily portable. It created a new market for small PAs operating in malls, foyers, sports centers - anywhere you could gather an audience of even just a few tens of people. And it only took one averagely strong person to put a couple of 802's on their tripod stands.
Now the bad. The Bose 802 used eight identical smallish drive units - neither big enough to do the work of a woofer, nor small enough to make good tweeters. They were great in the midrange however, and many people's perception of the 802 is that midrange is all there was.
Low frequencies suffered because the diaphragm of the drive units had to move in and out a long way to move enough air. It's far better to do this with a large diaphragm that only has to move a small amount.
High frequencies suffered because the diaphragm was too large to prevent bending and distortion caused by 'break up', which is where parts of the diaphragm are moving out while other parts are moving back in. Also, a large diaphragm is very directional at high frequencies. And when you put several together, the effective size is equal to the total size of all of the diaphragms added together.
The result was that the Bose 802 only worked even passably well when the specified equalizer was installed. However, many operators didn't understand this and used the system without the EQ connected.
Still, Bose sparked off the market so we'll give them credit for that.
Now there is plenty of choice in small PA loudspeakers. But they all still sound pretty bad, even though most use the conventional woofer and tweeter configuration.
But a loudspeaker designer is faced with the immutable laws of physics. Applied to loudspeakers, the laws of physics state that you can have a high sound output level, or impressive bass, or good sound quality. But you can't have them all together in the same cabinet.
So the designer has to decide which is most important, and naturally enough in a PA loudspeaker, efficiency and high output level are vital. The next priority is the impression of good bass. Note the word 'impression', as the ears are easily fooled.
Last in the list unfortunately is sound quality. The fact of the matter is that unless someone finds a loophole in the laws of physics as they are currently understood, small PA loudspeakers will always sound pretty bad.
Another significant point is that manufacturers also prioritize light weight. Unfortunately this means that the cabinet radiates a considerable proportion of the sound output.
If you want good sound from your PA system, then bigger cabinets will always be better for bass. Tweeters need to be as small as consistent with high output levels, or directional so that multiple tweeters can each cover their own section of the audience. The midrange, as always, can pretty much look after itself. And the cabinets that support and surround the drive units should be heavy and well damped so they don't radiate any more sound energy than absolutely necessary.
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