The entire Northern network seems to function without first class complications. Northern has many faults, but how many travellers from Corby really need first?
Surely post Covid EMR must reconsider spending money on something users will have had several years of not paying for before first can be reintroduced? Just ensure all users get quality seating.
When I commuted from Wellingborough in the 1990's (admittedly, that's long ago now) there was quite a contingent of first class season ticket holders using Kettering and Wellingborough. It's not unusual for the shires to have areas of affluence and that's the case in Northamptonshire. You may be surprised by the type and prices of property in villages where Corby is the railhead.
From their (often loud) conversations the employment of the 1990s commuters centred around finance and insurance (for example, being a Lloyds member), with the status that they needed to show their face in their office around 3 days a week and keep minions on their toes. Not candidates for working from home, but possibly they won't find the accommodation on offer (and the lack of opportunity for G&Ts on the way home) in the new service acceptable.
Of course, some will think their absence will not be missed or even welcome, but the revenue they provide might be.
Talking of Northern, there was once a strong market for first class commuting into Manchester (the 'Club Trains', for instance) all gone now. I have no idea whether the loss was caused by lack of demand or lack of supply, but in the East Midlands Electrics it seems it will be the latter. I can't see how it's realistic to expect first class demand to return after it's not provided for a period - perhaps a year