You might want to consider something more along these lines: You can move up to half your speed on an impulse, with a minimum of 5 feet.
So, a "cautious" approach could literally be 5 feet per impulse like you suggest, but a couple quick jumps into the fight could get you there much more quickly. If you know you still have a long way to go, when you dash, don't double the speed--keep it at half--but allow it for two more impulses.
Ex. You're speed is 40 (mobile feat). You move 20 on impulse #1, 20 more on impulse #2, but still need to more more so elect to take the dash action and gain another 40 feet of movement, allowing you to move 20 on impulse #3 and 20 more on impulse #4.
This shows how it took you "time" to move a full 80 feet because you covered the ground over 4 impulses. Additionally, someone like a rogue could use Cunning Action for that dash, and still have another dash action to take, allowing them to further move on impulses #5 and 6, covering a total of 120 feet of movement. Or, since they still have their action, the rogue could actually attack a target.