Using a grid can cause people to feel as if they are playing a board game (hex) or chess (grid). I say this for a reason, because people come to think in 2 dimensions without realizing it when using these flat systems. They do not readily facilitate 3 dimensional movement. Each turn for a character in a tight situation becomes a move in a grand master chess tournament requiring careful consideration. These are all just tools to help us accomplish our RP ends.
I would argue that ease of play is exactly what the tape measure adds. You are correct that it requires two hands to open the tape, but simply purchasing one that locks in place frees your other hand to move the figure. As UAE has pointed out above, you can do some trig to calculate movement upward at an angle, but why spend the time? I think we all agree that there are times when a grid is useful and times when it impedes play. In my experience I measure the distance from my Wizard on the stern castle to the tengu rogue on the mainmast yard arm and if it is within an inch, then it flies. If it is an inch or more away, it doesn't. This does require that the GM isn't a jerk and is consistent when measuring and adjudicating the measurements. Yes, you can lose or gain 5' of movement or range, but I would argue that the less than precise measurements occasioned by the diagonal movement on a square grid do the same at least as often.
My real concern is the two dimensional thinking our grid systems unconsciously overlay on our actions in game. My secondary concern is saving time. Lots of times it is impossible to physically build terrain that would fit the game table and we simply use numbers in our heads to adjudicate situations. I heartily recommend anything that speeds play but I do find that a 3D battlefield makes play more dynamic and is facilitated time wise by using "direct" measurement. As I stated above, I use grid and grid less interchangeably to what I believe to be that satisfaction of my players, and it has resulted in more dynamic, cinematic play at the table.