| The problem is that tab only gives you part of the picture. Like you say, with a CD you can figure it out, but that's still some time spent memorizing rhythms and dynamics, plus the work of finding a CD. What if you're playing something that hasn't been recorded yet? That won't come up for everyone, but it's a significant problem for some people. With standard notation you can just pick up your bass and play, no extra materials or learning time required. This assumes decent sight reading skills, of course.
One of neat aspects of tablature is that it shows you fingering exactly. This can also be a hindrance, since it may not be the fingering you'd choose, and then you have to translate from the tab to whatever it is you want to do.
Another one of standard notation's pluses is that it's universal. As long as your instrument has sufficient range to play a line, there's no translation when you go from one instrument to the other, or to singing.
Standard notation, which really needs an abbreviation, is also handy for composing, as you surmised. You can see how all the lines fit together more easily.
Tab is problematic when you need to communicate with someone who doesn't play guitar or bass. You might want to have a horn player play a lick you just came up with. They don't read tab, so you have to teach it to them. With standard notation, you just write it down and hand it to them. "Play this", you say. This is really a composing thing. Of course, it goes both ways. They may want you to play a lick, and with notation, they can just hand it to you.
Like you say, tab works. A lot of the time it does. Sometimes it doesn't. For a person who can read standard notation reasonably well, tab is a big hassle, since you need the tab, a recording, and time before you can play a piece at all. If you just want to learn songs by bands you like, you've already got the CD, and you don't need to be able to play it without any learning first. Tab is fine for that. If you want to work with others, standard notation is the quick, easy way to do that. | 
