It's true and I'd honestly rather him win a Stanley Cup just to get rid of that story down the road. I couldn't care less about Washington or even Ovechkin but I was glad when Washington won the 2018 Stanley Cup just so that the mindless talk of Ovechkin not being able to win a Stanley Cup would be gone. At some point one of the best players ever is going to retire without a Stanley Cup and it's going to be so tedious to hear the arguments that will ensue.
Oh it's very inevitable. You can even just compare the list of "non-Cup winners" that have retired recently versus in an all time historical sense.
Hockey is a sport, whether due to having 6 teams for a long time, and then like 12 where a lot of those teams were jokes, where pretty much every historical great got their Cups. Historically, the "best without a Cup" list was like Marcel Dionne and then....... Brad Park? Before Dionne and Park came into the League (both baby boomers born a few years apart), I have no idea who it even would have been.
You also had the no salary cap era of the 1990s, where the best players would generally find their way onto the stacked superteams at some point or another to get one, even if it wasn't the team they started with. Obviously Ray Bourque came ridiculously close to not getting one, but he was able to get one right at the end when he joined a stacked Avalanche team.
Now is the era of hyper-parity with the very hard salary cap and continued expansion has pushed the League up to 32 teams (even in say Gretzky's era, it was around 21) making it that much more statistically difficult for a given team, and thus any player on a given team, to win a Cup.
Just look at the recent retirees, team "never won the Cup" is getting stronger and stronger. Jarome Iginla, Joe Thornton, Daniel Alfredsson, Patrick Marleau, Henrik Sedin, Daniel Sedin, Ilya Kovalchuk, Henrik Lundqvist, Carey Price. It's just not a guy here or there, a lot of great players are not getting Cups just due to how things have changed.
It's pretty inevitable a consensus top 20 all time player will go Cup-less pretty soon, hockey is too much of a depth-driven sport to assume a great player is inevitably going to get a Cup now.