At what point are we simply re-inventing the wheel? If the general idea behind Bitcoin was to empower people to handle their own money, going down that route, it sounds more as though we've effectively just added another middleman to the existing group of financial middlemen
The problem is that you can't expect everyone to take advantage of the potential financial independency. Simply put, people are lazy and seek the easy way of doing things. Most of them might never use a non-custodial wallet.
Unless I've misunderstood something, I get the impression there's no real benefit to the average customer beyond what they'd get using fiat alone?
That depends on what you think that the average customer is more likely to value. For example, Bitcoin transactions are irreversible. Assuming that most merchants will use third-party payment processors, this probably won't be a problem if they have some refund policy like Visa or MasterCard. Otherwise, there are going to be a ton of complaints. Unless governments push CBDCs and negative interest rates, I don't think that ordinary people have any significant incentive to switch over.
Or do the benefits stack more on the side of the merchants who wish to receive payment in BTC?
That's a good remark. I see Strike as a necessary product for the transitional period where more and more merchants start accepting Bitcoin while users are slowly catching up.