The question is why is polio “a different beast” that would not allow variants?
Some viruses just do not mutate as readily as others. Flu viruses of which Covid is a subset, mutate very rapidly. Polio, measles, and some other previous scourges do not.
Natural immunity from a previous infection is already known to be much more effective at preventing Covid variants than the “experimental vaccines”. But Covid is a flu type subset and just because you had it last year does not mean that you will not get another form of it in the future. Fortunately the “variants” will typically be no more dangerous than other upper respiratory infections. The flu didn't disappear after the true pandemic of 1918 to 1919. It just changed forms.
It is worth noting that various variants of Covid have already been going around for millennia; we just called them colds and not something new and scary. Colds and Flus have been killing old and people in poor health in large numbers for millennia as well.
It took 47 years from the time polio was first recognized until a safe vaccine was developed for it. The first vaccine released in 1955 caused over 250 cases of polio during the rollout and it was discontinued until the issue that caused the problem was discovered. The same safeguards that are suppose to be in place these days should have already shut down the massive now failed experiment.
As India clearly demonstrated their are safe and effective treatments for the Delta Variant that work. And we have other treatments available here that work also, but many hospitals and doctors are still following outdated treatment protocols that are ineffective and result in death and serious injury. Why the CDC has not changed its recommended protocol to more effective treatments has more to do with politics than public health.