I don't think "one helicopter type" is at all comparable with "one main battle tank"
More like with with "one tracked armoured vehicle" which is clearly ludicrous.
NATO needs a different helo type for;
Training (2 types, surely?)
Battlefield Attack (one)
ASW (one)
Small Ships(one)
Troop/cargo/liason/utility . Arguably one dedicated type; Chinook or CH53 but you'd still need 2 others as variants of ASW and Small Ships (eg EH101 and Lynx) being common types you already have - albeit in very different variants.
That makes six distinct types with 2 variants. You might contrive an advanced trainer common with a small ships/liason and bring this down to 5. Below that seems impossible.