I don't think they're going to fix it, because it goes against the spirit of time-attack, where you're supposed to run without stopping, and not arbitrarily stop playing in the middle of the attempt.
Also, pausing can be abused to mitigate nerves and plan your movement. For developers it would be nigh impossible to police, so here instead it was designed in a way where you have no incentive to pause.

Still, I'm sorry you've lost your perfect run. What level was it on ?
If you didn't spend a lot of time, you'll most likely get another shot soon, but I don't know your progress.

If you're not supposed to pause then it's fine, but then they should remove pause because it is misleading IMO.

I lost in Warp Zone, I actually had time of 2:03 (you're supposed to have 2 minutes), I paused very briefly and didn't know pause didn't work.

Just a note, if you unfocus the game it will not tick up the timer (since 2.3). If you use the menu brought up by Esc, then yeah it will tick the timer.

I don't think we want to remove the Esc menu because otherwise there would be no way to terminate the time trial early without quitting the game.