Decidability of rank-k polymorphism vs. System F
The conclusion of [Kfoury &amp; Tiuryn 1992] says (emphasis mine):


  We prove that [...] for every $k\ge 3$ there is a typing of constants
  that assigns types in $S(1)$ such that the type reconstruction problem
  for $\Lambda_k$ extended by this typing is undecidable.
  Unfortunately, this result does not give any clue as to whether type
  reconstruction for $F_2$, with or without constants, is decidable.
  Our decidability/undecidability proofs use in an essential way the apriori information about the rank of types.


So, if you don't force constants to have certain pre-defined types of known rank, or if you don't have constants at all, the problem may become easier (than undecidable). The proofs rely on having constants that are forced to have certain types. (Of course, as you pointed out, Wells showed that the problem isn't easier.)