Oh okay, my GCV160 isn't like that. It's got an automatic throttle, and a choke lever on the carb itself. You set the choke, start the engine, and the ACRS automatically and slowly releases the choke from that point on, and after a few seconds, the choke blade is open. Neat system!
My GXV140 engine has the remote choke/throttle control in one lever, apparently like your GCV160. When I bought my Craftsman (with the GCV160) I thought I was disappointed that it had an automatic throttle...I wanted to control it! But after buying this Honda Masters mower used, with the GXV140, I'm finding that it's sometimes hard to keep that cable in proper adjustment. The guy sold me the Masters mower because he kept having choke problems with it. Indeed, it's been hard for me to keep the choke in adjustment. It seems that the most I can ever get that choke closed, using the handlebar control, is about 95% of the way. If I reach down and manipulate the choke lever so it fully closes the choke blade, the mower starts right up. I bet the problem with your GCV160 is that the choke doesn't quite close all the way. In my experience with the GXV140, even if the choke is just cracked open, it might as well be fully open, because it's got to be closed tight to be effective.
Personally, I like the designs with the primer bulb. Just like carbureted vehicles had accelerator pumps in their carburetors, some small engines have a priming bulb to make sure there's gas in there to start the engine with. Although my GCV160 now starts very easily, it also has a simple automatic choke. The GXV140, with a choke cable that needs adjustment, it seems that a primer bulb would be a more reliable design. Granted, once the choke is adjusted properly, it should work everytime, but it's hard to get that thing in its sweet spot it seems.
Does your mower have any sort of warranty left? Has it acted this way since new? I didn't even know Frigidaire sold mowers, but it can't be that old because the GCV160 engine hasn't been around for that long...8 years at the outside I think. Did you buy that mower new?