Yes. I'm not arguing they should be indistinct; just that blending character aspects does take place. Sometimes purposely- Flash/GL in Kingdom Come, GL in Superman TAS, etc.
But I think the elephant in the room is turf. Or rather, what's Wally's turf now that Barry is the Flash? After Flash Rebirth, I remember every time Barry cracked wise, there were complaints that they were "stealing" Wally's humor and giving it to Barry. Which is <lotsa not nice adjectives> crazy.
And here we are, 10 years later, and it seems like the same conversation: how do we box these characters such that Barry remains the decidedly retro, man out of time character? I know you aren't personally advocating that. But isn't it clear some readers are?