I never told you to use 1/2", I said 1/4"-3/8". And the reason is simple, it's about the ratio of metal to metal when welding thin tubing to thicker metal. I'll give you an example, then I'll give you my "rationale" for my position.
Your tubing is 0.060. If you use 1/4" plate, bevel 1/16" from each edge. That leaves 1/8" landing area. That is 2x the thickness of the tubing. When you weld something that is 0.060 thick, you can not get any penetration without burning through. Using 1/4" (or more) allows heavy penetration against the plate, with a tie-in to the tubing. This is very strong and allows the plate to support the tubing.
Welding 0.060 wall to 0.060 sheet gives you nothing to tie to. That weld will be very weak. In fact, depending upon how it's done, it will either be cold, or crack adjacent, and likely fail any structural stress test. The original was a stamped gusset welded on an assembly line and tied into the rails where you have cut it.
I literally just did this same modification 3 weeks ago for a friend of my son, on his KZ400. When I showed him the sample pieces (welding my approach versus the stock gussets) after saw cuts and stress tests, he was shocked (pardon the pun) at the weakness in the gussets. Had I known this topic would surface, I would have taken pictures as they would now be quite informative to the point.
Now, why do I harp on this? A few years back I was fortunate enough to be introduced to a local guy who for 28+ years has been building spec race car tube chassis's for NASCAR, SCCA, etc. The guy is a prominent builder. He was kind enough to make a subframe for me because a mutual friend took me to him. It was he, that explained the importance of suspension gussets and the flaw in the stamped gussets. So I follow his professional advice on frame mods, bracing, and material thicknesses without question as he is the expert.
I'll say it one more time; it's your bike, do as you wish and as you are comfortable. When I see something that I strongly believe is not prudent or sound, I'm going to speak up. Good luck with your project.