The first push mower I used had cast (or at least iron) wheels. And yes, it would slip, especially in wet grass. That would also plug it up very well, thank you.
We had to get the reel sharpened at least once a year. This meant taking the whole massive thing to a shop that did it (ours was also a shoe repair shop). I think the wooden parts were solid oak or hornbeam (ironwood) from the overall weight!