Well yes, but …
We certainly do have a problem with access to mental health care. As I know from much direct personal experience, however, so does the UK, where obtaining mental health care is stigmatized and tightly gate-kept. Even people struggling with suicidal impulses in the UK often find meaningful care difficult or impossible to access.
But the UK doesn’t have mass shooting.
Because very few guns circulate in the population.
Besides, access to mental health care wouldn’t have stopped the Uvalde shooting. Nobody suggests the shooter or his family even tried to access mental health care. Nobody thought he needed to.