The idea is sound.
Based on my experience, I've had several final battles that lasted around an hour, and in those, the correct move is immediately obvious, but since the timer isn't ticking, you can get distracted, switch heroes, change the music, or go make some tea =). I sometimes allow myself this indulgence, attacking one unit with another during my turn and moving away while my unit is in action.
Overall, I had a similar idea, but it needs to be implemented primarily as a preventative measure to avoid players getting distracted, so the timer should provide a generous amount of time.
What should be the principle behind such a timer?
For example, if it's feasible, 1 unit of HP equals a certain amount of time in battle. In a player-versus-player battle, the HP of all units at the beginning of the battle is summed and multiplied by the time cost, and each player is given half of the resulting timer, with a small amount of time added for each turn in the battle.
Also, what happens if a player doesn't manage to make their move – does the unit go into defense mode, or does an autobattle start?
In my opinion, implementing such a change would be difficult.