This can't happen just because it's bot-friendly. It's also alt-friendly. If you have to be online at the placard open at the moment a house is available to get one, then SE is limiting a single account to 1 chance at the house, and a single machine 2 chances at a house. If you can win a house while offline, suddenly any account can enter the lottery 8 times and people running multiple accounts on one system can enter with every one. Lottery gets suggested frequently, and unfortunately it would only make getting a house harder - though it would do away with camping.
SE won't do this because no one wants their games spying on their computer. Would it cost them many customers? It might, and might not even stop the bots in the process. It seems like kind of a gamble with their resources. As well as general spyware concerns, the ToS doesn't allow modding but people do it. It exists in sort of a 'dont ask, dont tell' space but a lot of people run reshade, texture, or data mods. If SE ran anticheat, they'd likely bar modding through the same means, and upset a lot of their customers. SE doesn't like to rock the boat and wouldn't implement this tool.
Your other ideas are decent. Though I think the timer should just be gone, rather than reduced. I think the price should be what it was in ARR: 40 million or so, closer to a house's genuine value. Supply will be increased just because fewer people will be shopping for houses if the price is increased. Right now you earn enough gil doing the storyline to afford a house, so many of the 20,000+ players per server want their share of the ~4300 houses left per world after FCs fill their spots in. As for 'more/instanced houses' we can only hope. The announcement of new wards back in August made it sound like more were coming once they had servers in place (not til travel is normal) but no one can say when or how many wards might be added. Instanced housing is a maybe, especially with ishgard on the horizon. But they've gone this long without it, it seems an unlikely turn to make right now. It's not impossible but I remain skeptical. I've heard that Yoshi P really loves the neighborhood feel.