I'm going to give you some reasons as to why comedy and music don't mix very well, and why Rebecca Mayes fails at what she tries to do.
The problem with musical comedy is that it usually boils down to watering down both art forms. In any type of music, if you choose to bring any instrument to the forefront (whether that be vocals, guitar, drums, etc.) the instrumentation that goes behind that cannot do anything too interesting lest it overtakes the "main focus" of the song. In most comedy music this comes down to the delivery of the vocals, and so all the music behind that has to be blander than the lyrics, as they are the focus.
In terms of the comedy being watered down, you have to find a metre of the line and stick to it so that the rhythm of the song is not messed up, and the rhyme scheme also comes into this. In this sense it is hard to come up with elaborate jokes that incorporate effective timing, which is pretty much the basis of all comedy. You end up with people trying to squeeze in bad jokes that they cannot elaborate on, which do not sound good in the context of the music anyway because they also have to worry about the aforementioned rhyme scheme, and usually (especially in the case of Rebecca Mayes) this doesn't really come into their thought process much. What you're left with is a song that sounds childish, and is a cut below any other kind of songwriting.
This is not to say that music should not have a sense of humour, it most certainly should, infact it is one of the most important things to convey in music. However, this is achieved a lot more subtly than simply singing bad jokes. Strapping Young Lad, for instance, do not sing jokes. They are, however, a very funny band. They mock the pomp and "seriousness" of the metal scene without it damaging the music, because it is never foregrounded. The music and production come first. It is simply in the periphery of the listener at all times. It is ironic that music that out and out tries to be funny in actuality is much less humorous than a band that simply poke a bit of fun at things that are on their mind.
Tenacious D are actually an effective example of comedy and music being mixed. They are seen as a comedy band, although I would say they were a legitimate musical group who happen to do comedy as well. If you listen to the first album, there are a couple of out and out comedy songs (which I believe are the least effective on the album), but the rest don't really have jokes, as much as it has lyrics that simply aren't that serious. The music is good, and there is a good sense of humour about it. The comedy in this case comes from the skits, which are very funny and well written. This is not mixing comedy and music as much as it is compiling them together. The music is decent, and the comedy skits separate to that are funny. If they were merged somehow, then I believe each part would be significantly damaged.
In all of these senses, this is where I believe Rebecca Mayes, and most other comedy acts fail. The mixing of music and out and out comedy puts too much focus on poorly written lyrics, and so ends up watering down both the music and the comedy.
Sorry for the rant, it is just something that gets to me. Plus there's also the fact that if Rebecca Mayes didn't do comedy I would still find her voice annoying as fuck. Also, if you're offended by Yahtzee then you clearly don't have a sense of humour and thus do not have any idea of what is funny anyway. Hope this helped.
