If I stay in an Ibis or Ibis Budget hotel it isn't necessarily because I only care about price.
ibis is part of LCAH, ibis budget is not. They serve different market segments. ibis is frequently ~50% more expensive than a nearby ibis budget.
It's more likely to be because all the hotels in a particular location are operating in that price category. In which case Accor might benefit from giving me a reason to choose their property over a Travelodge or Premier Inn.
I disagree. If in a location you have only lowest-budget economy hotels, there's a reason for that. Usually, the reason is that all but a few customers only care about price (and a basic level of cleanliness). It doesn't make sense to expend the resources so that you can take care of the few and far between status customers. (And even if you did, those few status customers may be highly budget-concious as well. They may happily take the status benefits but don't show you any loyalty if the budget motel across the street is slightly cheaper.....)
So, I don't think your point changes my argument at all. To me, it seems unworldly to complain that Accor's lowest-cost brands don't participate in LCAH.