It depends on who you get for inspections. In Australia (NSW) they are allowed to do 3-monthly inspections. I've never had someone look in my oven as one of these (that I can remember), but I do remember that the agent for our first rental just loved to have something to tell you to do. I don't like spiders, so keep the webs in the house to a minimum, but I can remember when we were 18 she came to do an inspection and the only thing she could get us on was that she found one cobweb in the house. She made sure to tell us to clean that up!
At our last rental it wasn't until we'd been living there for nearly 9 months and the landlord decided to sell the house that the real estate realised we weren't on their periodic inspection list. So they tried to squeeze a few in close together to get up their quota, along with showing the house to prospective buyers, in the 3 months before we tired of it and moved out!! They never complained about anything when they came through, but it was a disruption to our daily routine (homeschooling) and made the house feel less like our home.
We are currently renting privately. Have only been here 3 months, but I don't think our landlord is worried about inspections. They have been over a few times, to pick up their mail and that sort of thing, but haven't searched every room. They commented yesterday that they are really happy with the job we are doing onthe gardens. I know that it is important to them that we keep the lawns and gardens nice, as this is their retirement home. Luckily, a nice lawn is important to us as we want somewhere nice for our kids to run around.
On the topic of ovens, I did have a fire in an oven, once. We moved in to a house we had purchased and there was a very old oven there. Perhaps 30 years old. I was counting down the days until is stopped working, so I could get my dream oven, and it didn't make me wait long! The bachelor who lived in the house before us (in his 60s) wasn't terribly in to scrubbing the oven, it seems!
I don't find it difficult to keep an oven clean, so long as you start with something reasonable. Just a wipe out when you get a spill, and a deeper clean every now and then is enough. But having seen the oven at our last rental, I can understand why some agents are picky about it. The oven was only 6 years old and it was absolutely disgusting. It had been cleaned before we moved in, but there was only so much you could do once it was such a baked-on mess. I scrubbed it hard a number of times while we lived there, and did my first-ever "toxic, spray-on" oven cleaning when we left and nothing would budge that mess. I also wonder if the tenant had taken off with the racks from the oven, as the racks in the oven definitely didn't come with that oven. Any time you would put something on the rack to cook the racks (and your food) would crash to the bottom of the oven unless it was carefully placed just so, and you didn't dare to breathe while doing it! All that splashing didn't help with trying to keep it clean.