The more address types there are, the greater the chance someone messes something up when trying to create some 3rd party application, or otherwise. If you are a user of this 3rd party application, this will negatively affect you, and if you are a bitcoin user, this has the potential to reflect negatively on bitcoin.
First of all saying "3rd party application" suggests there is a centralized authority that produces bitcoin related applications and anybody else is a third party which doesn't make any sense.
Secondly if a developer is not capable of correct implementation of a simple encoding and by extension address validation, then you have so much more serious things to worry about in all parts of that application than existence of multiple address types and encoding algorithms!
Also, if you are trying to recover your wallet from their seed, having multiple address types adds complexity to the process, and may make some people erroneously believe there is a problem with their seed when they use their seed backup to generate the wrong address type.
That's the inherent property of mnemonics that lack address type indication (and a lot more such as derivation path). Existence of different address types is not a problem here.