I assume "gutting" the TS is analogous to just removing it. On some engines, like Merc V6 blocks (late 1990s 150 for a reference) the pee is plumbed off the output of the stat meaning the engine cooling water has to get to 143F to get the stat to unseat and let water out. This means that initially you have to wait for it and then when it first comes out it's on and off as the engine warms up.
Other engines are plumbed directly and as soon as you get a few # of water pressure you get pee. Changing from the former to the later on those engines is no big effort and I did it because I didn't want to wait.....just tapped into the bypass valve feed hose instead.
On removing the stats, or modifying the block cooling water per se, on the mentioned V6 and other engines surely, the stat is at the top of each cylinder bank and if you pull them out, and let water free flow, the top cylinder on each bank doesn't get fully covered in water at engine speeds below 2500 rpms (serv. manual number). Above 2500 water pressure (when the proper stat. is installed) is sufficient to force the bypass valve (popoff) off it's seat and allow full flow through the powerhead.
Side note: The engine in my Avatar, 2002 90, triple, looper, was purchased (with the boat) 2 years old. On my maiden voyage, I got out past the "no wake" zone and was putting around getting used to things and the Over Temp. alarm sounded. Didn't know what to do so I decided to punch it out to get some "ram" water assist to the impeller and once up on plane, a few seconds later it extinguished. Didn't reoccur until I slowed back down (below 2500 rpm). Short story....my stat was stuck shut (failed) and the bypass valve kicked in at the higher rpms as was it's design.
If I were operating in salt water, a new stat(s) would be an annual maintenance event!