True, thick coins are a problem (though I was able to get my Ceylonese dumps in cartons and album) and very large coins and especially medals as wel as orders and decorations are also a problem. For all these, trays are a solution, albeit more expensive, as you noted.
Another drawback of trays is that many are made for different purposes. As a consequence, some are made of materials that damage coins, such as young or "juicy" wood, felt-like "floor covering" containing softeners and glue that attacks coins (I have some educational examples

). Good brand names selling stuff for coin collectors are OK (though not available world wide), most old second hand coin cabinets are fine (and really expensive), but watch out for el-cheapo trays made in China. I have never seen any made in Russia, but wouldn't trust them, as it is one of the last countries still making coin vinyls and coin album pages with softener.
Peter