And halflings can bump their strength with levelling ASIs. But I think it is clear that wizards would struggle to be healers and it comes far easier to other classes, bickering about specifics doesn't change the overall picture. (And halflings were never bad fighters, they just needed to be dex-based fighters. They had to adopt the flavour that fit their species.)
It is not about right or wrong, it is about what the purpose of the rules is. If the credo is that everyone must be able to anything, and rules should not set limits, then why the hell are are we playing a game where species and classes are predefined rule packages? The literal point of those is to set limits.
If we have splats, they should define and limit things. If we don't want that, then don't have splats, have freeform character building instead. Simple as that.