Can playing chess alone without an opponent improve one's thinking ability and problem-solving skills?

I will assume playing chess alone without an opponent mean analyzing games all alone? If Yes, analyzing games of grandmasters and master players has proven to be one of the ways to improve a player’s analytical skills. However, there is a certain level a player can attain, after that, they get stalled and won’t notice any significant improvement.

The only way to know if a player is improving is to participate in tournaments. Like true motives, tournament will expose or reveal a player’s strength and weaknesses. Reading books, analyzing games and preparing lines as black and white will improve a player’s thinking ability and problem solving skills. These are like nice to haves and not the real deal. The real deal is in testing the waters, navigating the field and coming out tops or otherwise. With that, a player will know if they are improving and if there is more hard work to be done depending on their chess goals.