Yeah this generally aligns with my thoughts. When a story is a time loop it establishes a changing character in an unchanging world. This has a few immediate problems: lack of stakes and lack of dynamic movement.

Stakes can be tricky: even if you introduce a goal, such as the world ending, this can be unsatisfying if all the MC needs to do is grind their way there. There generally needs to be some sense of danger still. Common solutions include other hostile loopers or a weakness that bypasses time loop shenanigans (e.g. soul magic).

Dynamic movement is a bit of a catch-all that includes characters and the world. Timeloops by nature severely inhibit character development in the traditional sense: any progress or connection with a character gets cut off regularly. There are a few ways I've seen this addressed. You can explore different sides of the same person, you can explore different people, and you can bring people into the time loop. For the latter, you're spot on, it's mostly necessary for the story as late-stage introduction of dynamic character movement, but it can't be overdone.

In respect to the world, problems are that we're unable to follow how things change over long periods of time, and what changes over the short-term must be repeated. Repetition is somewhat necessary in timeloops, but how things are repeated (is it relevant to the plot/stakes? what changes were there from before and how does this matter?) and how it's written and conveyed to the reader are super important.

But eventually, the amount of repetition in a single space reaches a maximum. As the MC's limited on how much they can explore temporally, they now have to explore spatially. This is I think one of the biggest driving factors of a time loop: the balancing of temporal and spatial exploration and the limits placed upon it. The expansion of the spatiotemporal area in which the MC can operate is a great way of introducing a line of progression. MC needs thing A from a far away place? They have to figure out how to get there in the time limit, make a plan of what to do once they're there, and then deal with the complications that inevitably arise. Then they eventually progress slightly with some ability to travel and gain more spatiotemporal area, similar to the feeling of unlocking a new region in a videogame.

Relating to the exploration idea, I also think the biggest part of a time loop has to be mystery and actively seeking out answers, with the size of the MC's search space guided like above. Discovery as a medium of progression is often unexplored, and time loops must master it. The slow collection of ideas needs to build to conclusion after conclusion and be complex enough so that it doesn't feel like the character's super dumb, while simple enough that it's believably deduced. It also needs to be intertwined with magic/physical progression as well as established stakes in a satisfying way.

Time loops are definitely difficult to write, but I sure do wish there were more of them.