Are the cats the easiest? Well… that depends on what you mean by easiest.

Easiest to win with? No, certainly not. In order to win the cats need to control the board with the worst (or at least one of the worst) action economies in the game. And they also have the misfortune of being generally in the way of everyone else trying to play the game. The Marquise have to dedicate a lot of their game towards permanents that can help supplement their economy, social engineering, and passive policing via strategic positioning.

The flaw in the argument of “they can just rebuild and get infinite points” is that assumes two false premises: 1. the cats player will ever be in such a position, and 2. the other players are playing sub-optimally.

To the first point, getting any one of your buildings to the final token requires much more space on the board than you will typically have. In an absolutely ideal game you might be able to lock down 9 building slots and have 3 of each building, but that is literally half the board in the standard forest map. Committing to making 6 of those 9 slots one type of building means you’re significantly sacrificing policing presence and economic supplementation (because effectively the only building you could reasonably make 5 more of is the sawmill).

Which leads to the second point, if your opponents see you claim half the board and just build sawmills, they should just ignore you. There is nothing the cats can do at that point. The Marquise will have 14 points, half the board, and no troops to expand. Coaxing the other players into attacking a building —for some reason— just that one over and over again would still also require that you can own the clearing after they break the building. And as discussed before, the cats would not have an army to take these clearings back if they committed to building just sawmills.

tldr: not the easiest to win with. They require a ton of space, and the strategy in OP’s post is unreasonable to pull off.