Why is bottom-up parsing more common than top-down parsing?
If you choose a powerful parser generator, you can code your grammar without worrying about peculiar properties. (LA)LR means you don't have to worry about left recursion, one less headache. GLR means you don't have to worry about local ambiguity or lookahead.
And the bottom-up parsers tend to be pretty efficient. So, once you've paid the price of a bit of complicated machinery, it is easier to write grammars and the parsers perform well.
You should expect to see this kind of choice wherever there is some programming construct that commonly occurs: if it is easier to specify, and it performs pretty well, even if the machinery is complicated, complex machinery will win. As another example, the database world has gone to relational tools, in spite of the fact that you can hand-build an indexed file yourself. It's easier to write the data schemas, it's easier to specify the indexes, and with complicated enough machinery behind (you don't have to look at the gears, you just use them), they can be pretty fast with almost no effort. Same reasons.
It stems from a couple different things.
BNF (and the theory of grammars and such) comes from computational linguistics: folks researching natural language parsing. BNF is a very attractive way of describing a grammar, and so it's natural to want to consume these notation to produce a parser.
Unfortunately, top-down parsing techniques tend to fall over when applied to such notations, because they cannot handle many common cases (e.g., left recursion). This leaves you with the LR family, which performs well and can handle the grammars, and since they're being produced by a machine, who cares what the code looks like?
You're right, though: top-down parsers work more "intuitively," so they're easier to debug and maintain, and once you have a little practice they're just as easy to write as those generated by tools. (Especially when you get into shift/reduce conflict hell.) Many of the answers talk about parsing performance, but in practice top-down parsers can often be optimized to be as fast as machine-generated parsers.
That's why many production compilers use hand-written lexers and parsers.
Recursive-descent parsers try to hypothesize the general structure of the input string, which means a lot of trial-and-error occurs before the end of the string is reached. This makes them less efficient than bottom-up parsers, which need no such inference engines.
The performance difference becomes magnified as the complexity of the grammar increases.