Hah, no! I do wonder what these "run flat" things are, that people talk about. But it scarcely seems worth it for the very occasional puncture. Although I've had several slow punctures over the years, until the Hardknott Pass shenanigans I can only remember four absolutely-flat-get-the-spare-on incidents in forty years!
Runflat tyres are basically tyres with reinforced sidewalls, which enables you to run on them while they’re are at zero pressure (or flat). Some brands allow you to repair a puncture in a run flat, some brands don’t allow repairs as the tyre sacrifices itself while being run this way.
A rule of thumb with run flats is you can run them with zero pressure for max 80km at maximum 80km/h, or roughly for 50 miles, at 50 mph. Which in most cases gets you back to civilisation.
They tend to be less comfortable as the reinforced sidewalls have less flex in them and thus the tyre itself absorbs less shocks from uneven roads. They can also be more expensive as the construction uses more materials and they are often OE fitment for luxury cars like Audi, Volvo, and Porsche.
In your particular case it is hard to know if a runflat would be strong enough to withstand whatever ripped the sidewall on your “normal” tyre. If you suffered damage like that to an runflat I think it would still immobilise your car. But with the runflat having a stronger sidewall, a similar impact might not even cause any damage at all.
A final note on reinforced sidewalls is that you also get LT (light truck) construction on many off road tyres, which is a reinforcement but not to the extend you can run them with zero pressure. You see XL on certain road tyres now as well, which is the same sort of reinforcement, but again that’s just to cope with the increased weight of (luxury) SUVs nowadays, and not the same as a run flat.