I'd have thought the general public were more likely to consider both than the rail enthusiast. A member of the general public with little interest in rail goes onto National Rail or Trainline, sees the prices for the journeys, the rail operators change names so frequently so the companies have zero brand recognition, these companies are not household names, just made-up titles which change every few years. The general public don't know what particular class of train the companies run, what will turn up and what difference it makes, they likely just select on price, choosing the cheaper company.
Nope.
People choose based on criteria important to them. I agree brand is probably of low consequence, but there are basically three groups of customers on long distance rail:
1. Low budget requiring flexibility (competitor: the old banger)
2. Low budget requiring speed but not flexibility (competitor: road coach)
3. Higher budget, speed and flexibility important (competitor: BMW/Merc or air)
Those in group (1) will be directed onto LNR. Those in group (2) onto Avanti Advances, or LNR Advances if on a really tight budget. Those in (3) will rock up at the station and buy a walk-up ticket, or their work travel agency will do so for them.
It's incredibly effective market segmentation which grows the market, not true competition (which tends to just cause cost-cutting which is not always a good thing). And I'd be surprised if GBR entirely removed it - it's the pointless "save 50p" ones like TPE vs. Northern that need to go. Deutsche Bahn does it to itself, with cheaper regional-train-only fares, for example. Or Stagecoach "competing with itself" with Magic Bus (which came about as true competition, but has remained despite this no longer really being a massive thing on the routes concerned).
I would be wholly unsurprised to see "regional trains only", "not InterCity" or similar tickets on the WCML being a thing under GBR. And that, unlike the petty spatting over 50p, would be a good thing.