I'm NOT an extraordinary player in general, but I do pretty well with D.Va. In fact, my experience is that D.Va is actually more fun to play now that she has a weakness because you have to actually actively pay attention to the battlefield to make sure you don't get shot down.
But her DM ability and her mobility make her an extremely effective disruptor. You need to alternate between 3 basic goals: Either you act as a supporting DPS with your team, batting the enemy with your infinite shotgun rounds from a different angle while your team approaches from elsewhere, you act as a frontline shield for your DPS so he can mow down whoever he's trying to 1v1, or else you 1v1 the targets you can.
For that last bit, you have to work around the characters your fighting. Some characters you almost never want to engage 1v1, like Mei. Everything she does counters you. Or Zarya, who you can only take if she has no charge. But other characters can be fun to mess with. For example, a good Tracer will typically out DPS D.Va, but you can actually block half her shots with DM by timing it right. Your CD is a tad slower than hers, but you can DM her first burst, shoot her while she reloads, shoots the second burst, and reloads again, then DM the third burst, etc. This actually has me winning many Tracer battles even though she should tear me apart.