Sea Cat was a completely obsolete point-defence system at the time the Type 21 was new, i.e. for its time the air defence capabilities of the Type 21 were extremely poor. The same is true for their radars. In addition, with all the mentioned added weapons, the hull was actually overloaded. Limitations regarding the use had to be introduced and still massive cracks were common. No upgrades were possible. The armament had to be reduced to be able to continue to operate the ships. The Type 21 was one of the worst designs of its period - and there were many bad designs.
In contrast, Sea Captor is no point defence system, but can be used to defend also other ships. It is an up-to-date air defence system. The air defence capabilities of a Type 31 will be good (for a GP or ASW frigate, for sure not in comparison with a dedicated air defence ship), way superior to a LCS both in regard of the missiles and the radars.
A Type 26 may have the space to load longer range AAW missiles, but for which of those it has a suitable radar set? The Type 26 is optimised for ASW, it does not have the radars for a optimised air defence ship. For sure, the VLS launcher can be loaded with future weapons, but they have to be bought increasing the coast. In case of a Type 31, also the launchers have to be bought, but it would be still cheaper than a Type 26.
As you have written, the Type 31 is designed to be cheaper and it does include fewer systems, but when introduced the armament will be comparable to a Type 26 (based on what I know regarding what the RN actually has to arm a Type 26) and it still has a lot of capacity for upgrades. It is the much more sensible approach compared to the Type 21, which were designed to be cheap, but were more expensive than aimed for and had no capacity for upgrades.