So, for a nuclear plant to be profitable in a competitive market, it needs to produce energy for less than its competitors. If its competitors don't have to pay to capture carbon (through money or output) then they are always going to be cheaper per watt, and the plant is going to become unprofitable.
The only way that would work is if you had chronic electricity undersupply (v. likely but also pathological) or if nuclear plants were way more efficient than alternatives (the opposite is true).
Generally the argument for nuclear is you need a diverse range of energy sources to have a stable power supply, not that they are a great 'bang-for-buck' option. (An argument I agree with, fwiw).
EDIT, PS: It's worth keeping in mind that carbon capture is largely an unsolved technical problem, and I think it's perfectly feasible that it will never be solved. The basic idea of burning fossil fuels for energy, then using energy to recoup the carbon from the atmosphere, just makes no sense at all. There's no world where this would be cheaper than just not releasing the CO2 in the first place.