Nothing beats a scope in taking an initial look at a digital signal. A scope is useful to determine voltage levels, whether the transitions are sharp and clean, baud rate, and whether the protocol is normal asynchronous serial or something else. If it is normal async serial data, a scope can easily show the number of stop bits.
But a scope isn't so convenient to use for decoding mass quantities of data once you've figured out what's going on at this lowest physical level. Sooner or later, you just want to deal with bytes, not raw scope data.
I've used a scope to look at raw serial data, and I've decoded a few bytes of raw data by hand by looking at the scope display. But after an initial peek using a scope, I've figured out enough of the protocol to hack together a level shifting circuit and then start using a computer serial port for the rest of the work.
Maybe I'm just having an attack of "sour grapes", since my scope doesn't have a serial decoder built in. I can see some usefulness to one, and like the original poster, I'd appreciate it if someone has a pointer to software that can do a serial decode on a .wfm file or similar. But I really don't think that I would use it very often. Usually, I just want to work with the scope enough to figure out how to get bytes to a computer serial port, and from then on, it's easiest to put aside the scope and work with bytes.
One caution about logic analyzers. They only work well if the transmission line being monitored is working reasonably well in the analog domain. In other words, they can give you a misleading and incomplete picture if there is ringing, crosstalk, slow transitions, or other kinds of problems that only a scope can see. And the only way you know the logic analyzer picture is misleading is if you look at the situation with a scope. Keep that in mind if you're ever stuck with a situation that seems very confusing when you're looking at it using a logic analyzer.