One of the benefits of having all three of these tags is that, per the deleted-questions tag usage guidance:
You can also use this tag along with [specific-question] and [meta] to ask why a specific question on Meta Stack Exchange was deleted.
The same goes for deleted-answers, though its tag wiki does not reflect it at the moment. It's useful to have these here for meta-discussions about Meta. Because... Meta.
Additionally, certain bug reports pertain only to a particular post type. Take this feature request for example. This feature request only applies to deleted answers, and has nothing to do with deleted questions.
These more specific tags also house quite a few questions. deleted-questions has 1,013 and deleted-answers has 774 (at the time of writing.)
The deleted-posts tag (which has a measly 165 questions) is used for questions that refer to both deleted questions and deleted answers, much like the feature request you recently created. If anything, this is the tag that's less useful (and the low amount of posts tagged with it is indicative of that.) However, I don't think we really need to remove/burninate any of these tags - they're useful enough as they are.
There are a couple of outliers that use all three, some of which could be retagged... but maybe not the FAQ question on deletion, where having the additional tags improves visibility.
If we were to merge everything into deleted-posts, we would also be intentionally making things less specific. This merge would also merge, at the time of writing, 1,655 questions into one much smaller tag for no real gain. Additionally, this tag's wiki is a bit lackluster...
So... Eh. I don't really see the harm in having all three. It allows for specificity without going overboard.