From my number of posts you may question my experience, but I have soldered that hole shut on several carburetors including one on a gasoline RC airplane engine. In my opinion a good solder job would be the most secure of the options listed with tape being just plain a bad idea. The choke plate is going to be subjected to a spray of gas and air, even though it seems it is on the clean air side of the carb. I have never seen a carbureted engine that doesn't experience spray-back/stand-off at some combination of load and throttle opening. This gas mist being sprayed back onto the choke plate will dissolve the adhesive of most any tape, some quicker than others. I would not want even a piece of tape ingested by my engine.

As to why some carbs don't have that hole or slot. On those carbs the choke plate typically will be spring loaded shut and allowed to open some once the engine fires.

Hard to choke. Solder gets my vote, from personal experience.