In 1e the Bard followed the path of being a Fighter/Thief at first. One of the stipulations of that time were that Thieves could NOT be Good. Afterall, the thought was that thieves main focus was...thieving. Taking things unlawfully from others was not seen as good (ironically though, I think you could be lawful neutral...which would be...interesting).
(In theory though, it would have made a LOT MORE sense for them to not to be able to be LAWFUL...which is what some thought at the time...which...kind of could be reflected below)...
Then, after you got to a certain level, you dual-classed or had a special rule for multiclass characters to become a Druid. Druids also were supposed to be neutral...aka...not good (OR evil).
This would imply that Bards were more of a neutral type character (though you didn't specifically have to go that route, depended on DM interpretation).
In 2e Bards were changed to a full class that were independent on their own, but were a subclass of Rogues. Rogues included Thieves and other such things, and of course, as I explained above...in 1e Thieves could not be good (though, I think in 2e that changed and they COULD have a good alignment).
3e had many things that were tossed in because of tradition. They were trying to appeal to older gamers, especially those from 1e who stopped playing when 2e came out, or who had drifted away with all the 2e Complete ideas as well as the 2.5 ideas. (of course, they also wanted to keep those players from the 2.5 era as well, so they also had items that reflected those, but it was more of a cross sectional thought).
So...the long round about thing I'm getting to, is if you have rules that reflect something like an alignment requirement, in many cases it was simply due to "tradition" of the idea.
It's why you also had certain rules on Paladins, Monks, and other classes in relation to who could be one and multiclassing as well as alignments and such.
It was also what led to the idea of favored class, or for more strict DM's, the optional rules inferred in the DMG of actually restricting class to certain races ala 1e and 2e.
TLDR: Traditions and nostalgia...