I think people are forgetting how big of a thing that is - the only non-Targs to EVER get Dragons are the Velaryons and that was ONLY because the woman who SHOULD have been Queen married their head AND they were ridiculously rich AND they are the most Valyrian after the Targ themselves.
Giving Martells dragons would just be a no go.
I mean to be fair, Aegon, Heleana, Aemond and Daeron in canon all get dragons, and while yes they are children of king Viserys, they are also the children of the Hightower daughter of a second son, and were not even offically expected to ever take the throne since Rhaenyra was heir and had children.
Here, Heleana and Aelora are also likely to get dragons of their own despite house Westerling being less prestigious than house Hightower and while the twins are still not expected to inherit the Iron Throne.
So I don't think it's really true to say the Velaryons are the only house to ever get dragons, nor that they only got them due to being extremely powerful, thus making our Martell children free to also get dragons.
Sure the Reach and Stormlands have bad relations with Dorne, but given that we are Heir, and expected future Queen of the Seven Kingdoms, along with the fact house Martell is as powerful as Paramount house, I think it's fair to say that if we want our kids to have dragons, we can give them dragons.
I do see what you mean though, mayhaps not all our children SHOULD get dragons, but I felt the need to clarify that if we really want, then they all COULD get dragons.