The alternative market based way is to a have an additional "capacity market" for which providers offer bids for committing to provide future capacity. Thus providers who can guarantee they will provide a certain capacity are compensated for it, without needing to have a shortage of electricity to make the dynamic pay out. This is how it is done for the rest of the US.
Texas uniquely forewent the capacity market as a subsidy for wind, since wind providers are unable to supply guaranteed capacity and thus unable to bid in the capacity market. This creates a much more raw dynamic where grid capacity is fine right up until it is not.
If I'm not mistaken, customers have little idea that a price surge is in effect and what the rate is until they get billed. It's not like going to a gas station, seeing a price, and being able to opt in to the transaction, seek alternatives, or plan to self ration your consumption, as you're prepaying for the energy. The way the Texas model works it seems to assume that customers have a financial buffer that they're able to tap into to pay the higher rates. Everyone should plan for such a buffer but for those that don't have one it places hardship on them. It's also a risk for the provider that they won't get paid their windfall. You can't send huge surprise bills and expect people to pay them.
A sensible approach is to charge a bit extra under normal conditions to build a communal buffer that is used to pay for emergency power production. As long as there's good governance, this derisks the system. Another alternative might be energy bill insurance, if such a thing exists. It's easier to plan for a fixed monthly premium than a surprise payment in an emergency.
I agree with your "sensible approach". On a side note, this issue is much like the reason conventionally taxis normally charged more than Uber did, but Uber had surge pricing. If you want enough capacity for the peak times, you need to overcharge at all other times.
The consumers who had been hit by this were the ones who opted in to receive power at the market rate from a handful of shady businesses. They explicitly had to change their service to this model because the TikTok ads told them that the current market rate is $0.02/KWh so they are "overpaying" if they are buying at the utility's price.
The utility rate was not always fixed/negotiated: there's at least one utility company (Griddy) had an arrangement to pass-through market rate + small premium. Before the storm, this mostly meant getting rates modestly lower than the competition. The same customers were exposed to the power market spikes and received bills over $10,000. IIRC, Griddy has since filed for bankruptcy as the Texas legislature was generally supportive of individual customers not paying their bills. Paradoxically, Texas's political leadership allowed the utility companies to recover their losses by billing customers over years, which seems mostly performative/hiding expense from customers, but still decoupled from market forces.
The alternative, non-market way would be to guarantee revenue even in times when the excess capacity isn't needed (most of the time), by paying more than the spot market price would normally provide. Personally, I prefer that way. But, if you're using a market system for electricity, you need an incentive to build excess capacity. Then, when a non-market mechanism (the order to impose blackouts) interferes with that, you need to make up for that somehow.
Again, I'm not saying I totally buy this, but there is the rationale.