A less-specific vaccine would create immunity against multiple targets, and would logically require more simultaneous mutations to create an escape variant.
Unless your goal is to sell a new vaccine every year (chase your own escape variants, immunity-as-a-service), then MRNA isn't obviously a win.
However, create a population with narrow immunity based on a single protein, and you create a selection pressure that incentivizes mutations in that protein. Once a successful mutation exists, it has a wide open field to spread unchecked. With broad immunity (multiple proteins) it is much less likely that a variant can realize the multiple simultaneous mutations that would be required to spread effectively.
1) Not all sections of a virus mutate at the same rate. Some sections of a virus are highly conserved or the virus simply dies. In Covid-19, for example, the spike protein seems to be difficult to change significantly as it provides the primary entry for the virus into cells.
2) mRNA vaccines tell your immune system "target this specific sequence" and can avoid problematic sequences.
Normally, you have no idea what section of the virus your immune system locked onto. Even worse, if your immune system grabs onto something common (EBV pieces causing MS or alpha-gal from a tick bite, for example), it can hose you bad.
I am awaiting the trials on the ones that actually provoke immunity in the respiratory mucosa. It would be very nice to not get Covid at all.