Good info, The Gift Of Fire!
Based on what you've said and what I've been reading, I think the state of play is something like this. Feel free to fact check me since this *really* isn't my area of expertise.
Assuming we're only talking about the mRNA vaccines, repeatedly boosting will have rapidly diminishing returns. The mRNA vaccines only provide the mRNA "recipe" to generate the spike protein portion of the SARS-CoV-2 virus. Due to the huge success of the original vaccination programme, most immune systems have been imprinted towards the original Wuhan strain, making bivalent boosters (or even any theoretical future monovalent BA.5-tuned booster) ineffective in generating sufficient BA.5-specific neutralising antibodies to prevent the virus gaining a foothold.
Of course, with sufficient repeated exposures to the various Omicron subvariants, B cells could become increasingly tuned towards the new subvariants via affinity maturation [1].
Nevertheless, at the individual level, it seems that the T cells have sufficient immunological memory to provide protection against an infection severe enough to result in hospitalisation or death. Especially in the case of hybrid immunity (combination of vaccination and prior infection). The immune system would have been presented with sufficient SARS-CoV-2 epitopes via infection - not just the spike protein - many (some?) of which are preserved across variants/subvariants, making COVID-19 a relatively mild disease for those who aren't immunocompromised.
Putting it all together, the most likely outcome at the population level is a persistent low level of infections, with occasional spikes as new variants/subvariants reveal themselves. But these won't cause a surge in hospitalisations/deaths since most of the human population no longer has immune systems completely naive to SARS-CoV-2.
Unless, of course, a new variant emerges with enough mutations to evade T cell immunity...