Yeah that can happen. The problem is the aluminum piston is made of aluminum in order to keep the weight down, less counter weight on the crank is then needed and a smoother running engine. Aluminum expands quicker and more so than steel. So, if the tolerance are not right , say the piston is a tight fit, then you gun it, pistons heats up faster than cylinder which is air colled, piston rubs , usually the piston skirt, on the sides of cylinder, as well as the top piston causing the rings to press harder on the cylinder walls, piston overheats and starts to expand alot and thus seize. Sometimes it can ruin the piston. If its a steel cylinder, nothing will happen to the cylinder, worst case get a brake cylinder or small engine honing tool, Sears Cheap!, and run it very lightly with a drill and some light oil. The piston, could even be smoothed out with 600 or 800 sandpaper under water.
As an example. Found a briggs pressure washer 5.5 hp seized. Looked brand new. Owner ran it with no oil. Steel cylinder, aluminum piston. I cracked the case open, squirted WD-40 oil all over the inside. It was tight on the crank connecting rod. It losened up and after a few flips spun free. Cylinder still had factory honing marks, a good sign, piston had just a few almost unnoticable lines, quality aluminin alloy piston. I could have pulled the piston, wet sanded it and ran a light hone and new rings but didn't. I did pop the connecting rod end cap off, no metal, just a little scorn but it did stop running and seize now, remember. I just wanted to make sure no aluminum was on the crank and the oil hole was clear and unabstructed. Put it back together, oiled it up and ran it. Started fine, ran fine, I checked the oil and so long as the oil is fine, never had a problem with it. After ever tank full, oil went from full to half, with ever tank full of gas, the oil needed to refill usage decreased to now where every 6 full tanks of gas it needs oil. It rings reseated and no problem.
Also had a rider 12hp briggs. The crank oil seal gave way, owner didn't know and the engine seized. They gave it to me free

The crankshaft had melted aluminum and brass from the crankcase base bearing. I sand blasted the crankshaft journals, yes, to get the aluminum off. Then using very fine emory cloth and a drill, I polished the crank in minutes. Got a used good Crankcase base. Honed the steel cylinder and sand blasted the piston, then wet sanded it with 800 paper under water carefully to remove the up and down scorn lines not from the lack of oil but from the 13 plus years of use. Honed the cylinder, new rings and oil seal of course and that engine ran perfect with no oil burn what so ever. Compression was unreal, power was awesome.
The point here is the tolerance and/or quality or make of of the aluminum used in the piston and rings. If its cheap aluminum or aluminum alloy, it will have different expansion qualities and it won't withstand the heat and pressure as that of a good quality alluminum alloy will. Back in the early 80's american auto makers had problems with aluminum cylinder heads and their attempts to compete with jap car makers. They didn't have the manufactureing process or correct aluminum ally part right, thus warped heads and cracks as well. Now no one would blink twice at a car with aluminum heads regardless who makes it. Infact high output and hi preformace cars have aluminum heads and some crank cases. Briggs used aluminum cylinders in their engines at one time, short only a few years runs, and that lasted but a few years, they wore out quick and were just not durable enough although today scooter aluminum cylinders have that Nicasil plating, I would go still go with steel cylinder.
Model Airplane engines, large one at that, were 2 stroke ABC engines which meant Aluminum piston running in a Brass Cylinder that has been Chrome plated. The tolerances were so perfect that No piston ring was used. As the engine ran and warmed up the aluminum piston expanded more than the cylinder and created a seal with very good results and high compression. Later some makers tried to cut costs with AAC and it didn't work well.
So, yes break it in easy is always safe, but not always true. The ebay seller that sells Tiawan honda racing parts says the maker of his cheapo steel big bore kit is his exact words
"KH,this maker are Piaggio,Stage 6 and MRP supplier.
CMR and FM also from this maker."
Basically he said this manufacture KH makes cylinders for these companies which I would believe. I am not so concerned with the quality of the steel cylinder, steel is steel, you can grab a dremel, port it urself, rehone it and what not. But if the piston is a cheap aluminum cast alloy, the piston will fail with abuse much quicker than a quality one. There is a website that sells cylinders no pistoon and pistons. They have $18 pistons and $65 pistons, obviously there is a difference.
Sorry for the rant on 2 strokes but info is knowledge. I started thinking about my cheapo ABC model engines and my expensive italian Rossi's and I had to go with the Polini Corsa. Mean I will have to wait another month or two ($$$) before I can order the muffler and Variator but I will at least rest assured I have a ported high quality cylinder and I ordered a generic final gear set. I will go 3/4 throttle , add some oil in gas and yeah not be too hard but I will also run it open up for short bursts as its improtant for the new cylinder to reach maximum operating normal temp for a good break in. Example, you wouldn't run a cold engine full throttle, you would damage it, casing accerated wear. But once broken in, and at operating temp, you could throttle up and leave it there, technically, with no added wear.
I am just not familiar with these 2 stroke hondas and the quality of the kits, I will compare the OEM against the polini when I get it.