I live in Rugby and getting to Leicester by train is an absolute sod
Whilst this proposal may not be the best use of money, is also not likely to be too crazy a use either.
If, as a country, we wish to get to net zero then we need to do something about increasing the ability to use rail to link between places (especially where the amount of works are limited as it can use existing lines).
The more routes which are easier to go by rail the less need there is due people to own cars.
Whilst this one scheme may not have a significant impact on that front, if other similar (fairly easy to implement, with fairly low risk, at least compared to a new line) schemes are also progressed then the cumulative effect could be fairly significant.
As to passenger numbers, given that since the 1990's rail use had doubled, what at the time may have been a train with 40 people on (assuming a pair of coaches that's not even 30% full, so lots of pairs of seats and maybe a few table seats with just one person), even if assume +50% that's over 40% full.
Whilst that's still not overly busy, it does show that just the change in expectation in rail use could mean that there's enough demand that it's worth considering.
With the advent of online travel planners it's likely that any such new service could get spotted sooner but those who would benefit from it (again reducing the risk).
The other thing to consider (and although I've been to Nuneaton several times for work purposes, I'm not local enough to know) is could this have other benefits, such as for freight or for possibly allowing XC to run extra services that way from (say) Reading to ease their significant capacity constraint to more services (i.e. Birmingham)?
If (and it would probably require other schemes) the latter was possible it could improve frequency of XC services South of Coventry whilst also improving connections between parts of the East Midlands and parts of the South East. (To be clear I'm not saying that this must happen, rather could there be other benefits which could come about from this scheme?).