Why do I cut it off? I dunno really, other than it's an old habit from dealing with cars where they hung up or the hole needed to be opened up for one reason or another ie; no bypass path in the system. Never had it happen on a Supra though. Ran jiggle valves for years on mine without a problem before I started snipping them. On this car it doesn't seem to be a big deal either way.
I do wonder how many cooling systems suffering trapped air are a result of leaks combined with the valve not being installed at the top though. I've seen many a thermostat that was put in wrong. The valve is there to prevent air locking of the thermostat ie; if a large enough bubble builds up behind it, it won't sense coolant temp and may not open until much later, if at all. If the system has leaks it'll draw in air every time it cools off. That usually involves the overflow plumbing because since it doesn't operate under pressure people tend to neglect it. The path from the radiator neck fitting to the little strainer in the overflow tank must be airtight.
For noobs here's a bit about cooling system basics:
http://tinyurl.com/yvhn9l