I did the coach/timekeeper thing way back when, and I strongly believe it should NOT be allowed. The timekeeper has the opportunity (at least to an extent) to communicate with both the judge and the competitors in the course of a round, the exact type of thing that non-team members are NOT supposed to be doing.
My problem with this Motion is that many teams I've worked with/on don't have a lot of spare participants. Back when I was in college, one of my team's alternates (aka our timekeeper) didn't show up at Regionals. Competitively, we weren't affected -- but we didn't want the appearance of one of our witnesses acting as a timekeeper. Thankfully, another student from our school who was not competing that weekend agreed to fill the gap. Adoption of this Rule would prohibit that sort of assistance.
I agree that timekeepers necessarily have to communicate with the judge(s) and participants, but their communication is limited to stating times in open court. I do not think (and have not seen) a situation where a non-roster timekeeper actively coaches or otherwise violates the "No Communication" rule. Maybe others have....but, if so, I think there could be better ways to remedy the issue.
For many larger teams, I suspect that finding a timekeeper isn't difficult. But for smaller programs or those that do not keep many extra participants around, this Rule could pose problems.