The key word here is 'cold war'.Why is it not necessary? Overwhelming numerical advantage would be one way to achieve hard power that china needs.
China shouldn't use USAF as guideline on how many j20s it needs. If it can produce 100/year at lower unit cost, then it should do so.
The current US dedicated air superiority fleet is half that number, and more than half of it - retiring F-15Cs.
The second threat is overinvesting: while having a sudden qualitative edge through the 2020s is a boon, late 2020s are likely to bring in NGADs(two of them).
The idea is, multi-role fighters aren't exactly much weaker than (more) dedicated types. For example, I think that's one of the reasons why J-11D died (and J-16 went on).If you have more air dominance fighters than needed to achieve air dominance in a fight, you can always use them to delivery air to ground munitions, especially if said air dominance fighters are VLO. OTOH, if you don’t have enough air dominance fighters and the enemy achieve air dominance, all your bombers are just really expensive targets for the enemy now.
The difference is more towards the effects of specialization - and those are ultimately secondary.
More dedicated types can give an advantage at, say, secondary theaters - where the theater capacity is limited (you can deploy only so much), or, say, there is not enough force multiplying assets.
Basically - overinvesting in J-20As IMHO should be done only in case we really, really fear that late 2020s may be interesting. Otherwise, they shall take their organic spot in PLAAF, and leave more space for a more affordable type.