Yes, height restrictions are - by necessity - completely arbitrary. It could not work otherwise. Lemme go reductio ad absurdum - if the limit is, say, 48", someone will make the argument that their 47" son or daughter can safely ride, and that's possibly true. It's only an inch, right? But ... if someone 47" tall can safely ride, what about someone 46" tall? Only an inch, right? And then ... well, you get the idea.
What also galls me - and let me be clear, I am not referring to anyone on this thread - is the people - mostly parents, who supposedly care about their children's health - that think they know more about the proper safety procedures of a multi-million dollar (over $200 million dollars, in Spiderman's case) ride than the very highly-trained engineers that built the darn thing. Go on son, wear extra socks, and platform shoes, and stand on your toes, and don't worry, if you're thrown from the ride, well, we'll just sue! That's what I call "Winning the White Trash Lottery" (like those bozos in Detroit who are shocked that when they throw beer into the face of a huge man they might get punched. Oh, the pain and suffering!! Where's my cell phone - gotta call one of those lawyers I see on the tee vee late at night).
And for those of you who think I'm being harsh here, I invite you to spend just one day in the shoes of the entrance attendant whose job it is to turn those not tall enough away. You want abuse? Insults? THREATS? I know, I've been there. I can guarantee you not a day goes by at US/IOA or Disney without at least one ride op being reduced to tears by screaming, red-faced "parents" accusing them of ruining their whole family's vacation by not allowing little Dakota or Madison on the ride ...