This was a weirdly aggressive comment.
The solution is the pre-planning, which does not need a timer, nor is it a guaranteed result of a timer.
You cannot make players pre-plan. The timer encourages pre-planning, or at least rapid decision making on the fly. Both have the desired result of the game moving at a quicker pace.
It also has the benefit of creating an impartial tool for measuring, instead of relying on subjective "You're taking a long time." It is harder to argue with a clock. This is an advantage.
There was a problem, and in trying to fix it, the DM created a second problem.
What is the second problem?
No amount of nudging will make some players do anything. Some players are obstinate and frankly not very good, but honestly the solution to "this player won't stop looking at their phone and their turns take forever" may be to remove them from the group.
I don't want to wait 5 minutes for someone to dither and dither and finally decide "I attack"