There are still tons of things unique to Wally that would still be the same without Barry. I think it would be a terrible idea to do that, mind you, just like it was an absolutely terrible and disgraceful thing to do to Wally for the sake of making Barry the only Flash.
It's not actually complicated. You just do the DCAU show version. Never acknowledge Barry. It's not a matter of simple. It's incredibly simple to just ignore something.
It is 100% due to respect. Or bias, more than anything, from a single man who had a vice grip on the franchise since 2004.
Also Barry is NOT the first Flash. This is kind of what I'm talking about.