I know that for wh-movement out of a non-root CP successive cyclic movement is needed, so moving to spec-CP of the lower CP and then from there to the root-CP, but what's the specific restriction on wh-movement which leads to this requirement?
Successive cyclic wh-movement is motivated by theoretical principles of minimal computation, as well as empirical data. There's nothing inherently wrong with the 'one fell swoop' analysis, but cyclic wh-movement is preferable.
At any point in the derivation, the range of visible syntactic objects available for computations (e.g. Agreement) is restricted. Remember, SMT assumes that derivations form interface-interpretable objects as efficiently and lazily as possible. Thus, we assume visibility is restricted to phase (CP and vP) edges, which rules out one fell swoop movement. This is known as the Phase Impenetrability Condition.
The following data comes from McCloskey 2000. In a dialect of English spoken in Ulster, the quantifier all can attach to wh-pronouns.
Where all did you go yesterday?
Who all did you invite to the party?
What all did you eat for breakfast?
all can be stranded
Where did you go all yesterday?
Who did you invite all to the party?
What did you eat all for breakfast?
So it would seem that after [DP where/who/what all] merges in its theta position, wh-extraction can target only the wh-pronoun.
Turning to long-distance wh-extraction, the following are all grammatical.
Who did he say that he met all?
Who did he say all that he met?
Who all did he say that he met?
Assuming the copy theory of movement, cyclic wh-movement is further supported by languages in which multiple wh-copies are pronounced. Consider the following Afrikaans data from du Plessis 1977
Met wie het jy nou weer gesê met wie het Sarie gedog met wie gaan Jaan trou?
with who have you now again said with who did Sarie thought with who go Jan marry
'Whom did you say again that Sarie think Jan is going to marry?'