You can purchase a 3090 for $1000, assuming you're going to use it 24/7, at 450W you would use about 1000kWh, at $0.10 / kWh, it would pay itself in about 3 months.
That's not a typical use case during development though. People need fast feedback loops: they'd rather rent multiple GPUs and have the result the next morning, than waiting for days with no guarantee of success.
So unless you have stable tasks that need to run continuously, or have enough users to keeps your GPU clusters busy, your GPUs usage would be quite bursty: some period of high activity then a lot of time idling.
I'd argue the opposite. Having to spin up and down instances for development is a huge PITA, the tooling sucks, and the instance might not even be available the next time you need them. It also stresses me out personally, because I'm worrying about getting productive use out of every minute. Whereas my little GPU cluster (Despite a big upfront cost) costs nothing but electricity and runs 24/7.
I agree that buying is a good choice, but your calculation is wrong. 3 months of renting will take 0.2*24*30*3=$432, which won't even cover half of the base price.
So you save 500$ on cloud costs, spend 4k on developer time and delay a 250k dollar app launch by 2 weeks.
When you're just messing around, this is great. Home brew gpu labs are fun and cool. As soon as you bring economics into it and start valuing time, it's a non-starter.
So unless you have stable tasks that need to run continuously, or have enough users to keeps your GPU clusters busy, your GPUs usage would be quite bursty: some period of high activity then a lot of time idling.