Operational question about pitch for speed modes in initial climb out

Hi all, Hoping for some real-world expertise here. So I'm departing from an airport that has relatively low altitude restrictions in the SID for some time after departure. VNAV kicks in soon after takeoff and gets me up to 5000' or thereabouts at a fairly steep pitch angle which is to be expected on takeoff. Having leveled off at 5000 and sat there at 250 knots or so for a while, we're at some point going to get clearance for a further climb. I can do this with LVL CHG or I can stick in VNAV, and hit that little "continue climb" button (forget the name now). But seeing as we're still below 10000 and the aircraft knows it needs to stay under 250, this results in a massively steep pitch angle as the engines go to N1 - I've seen 12, 15 degrees of pitch a couple of times. My question is - in real life, is this how it would be done? I only ask because it seems like it would be a quite dramatic "leveled off, then suddenly really steep climb" sensation for the passengers. I guess the faster you get to your assigned altitude the better for ATC and your fuel flow, but I can't remember experiencing this sort of departure as a real life passenger. I could well be misremembering though... Appreciate any thoughts!