(This probably will be unpopular answer but oh well) I think that discussed rate limit on asking questions is worth keeping even if we ignore anti-spam considerations.
To start with, system already makes it much easier for these users to deal with asking rate limit. When they join another site they are automatically granted 100 reputation points as an acknowledgement of their familiarity with network-wide system basics.
As a result they need only 24 rep points more in order to remove new users restrictions and be able to ask at unlimited rate. That's just a matter of 3 answer upvotes or 5 question upvotes or 12 approved edit suggestions (or any combination of these).
This is already five times easier than it would take to total stranger (who would have to gain 124 rep points) and I believe it is good enough.
Also, underlying reasoning for suggesting to remove rate limit seems to be that high reputation at one site somehow helps ask better questions at another.
Per my observations though this is simply not so. If you give a read to this post and comments under it you'll find multiple examples of users having thousands rep points and years of active participation at one site asking blatantly, offensively inappropriate questions at another.
Currently top "outside reputation" of the listed abusers is about 16K and there seem to be no indication that it can't get higher (that list, it's steadily growing).
In the light of these observations removal of asking rate limit doesn't make good sense neither for the target site (which would be exposed to risk of getting its front page flooded by inappropriate questions dumped at unlimited rate) nor for these users from the other site who could bump into question ban due to having multiple (quickly posted) questions voted down and closed and lose the ability to learn and ask better questions.
Summing up, I think question timer is worth keeping anyway as it is useful both for the target site and for the askers and the bonus reputation already provides enough help for those willing to ask at unlimited rate.