Plenty of properties will advertise "no pets", but you can negotiate with the landlord about that. For example, you might offer an additional deposit against pet damage, or offer to pay a cleaning fee when you leave. I have pets and I have always been able to talk landlords out of their "no pets" policy.
If you offered the landlord double the lease price in exchange for a 2 year contract, will they take it? Almost certainly. Few contracts of that type are truly take it or leave it. My point is not that 2x would be fair, just that you have the ability to negotiate, which means the question of whether you can get a contract with the terms you want depends on your ability to negotiate a price for those terms.
Many landlords value stability and will be happy with a longer term lease at the same price, or even a lower price. And that's where the negotiation comes in. If the landlord believes prices in the area will rise steadily, then he may or may not want to offer a fixed price over a 3 year lease. Perhaps he will offer a longer lease, but with a stipulation of 3% price increase per year. You don't believe prices will rise that much, so you counter with 1% YoY. It's like buying a housing future. You're locking in the price of housing now as insurance against it changing in the future. That should properly have a different price than a lease with no such provision.
If a person believed in rent control, why not go further? Fix the price of property itself so that it may not rise more than 1% per year. If you buy a house from someone, the sale price may not be greater than the last sale price increased by 1% YoY. Would this be desirable? A law like this will have all sorts of negative consequences on the economy. For example, imagine a house owner who no longer wishes to live in the city. If prices were allowed to rise, then he's incentivized to sell his house, cash out on the increased price, and move somewhere else, enabling a person who wants to live in the city can do so. But if prices are not allowed to rise, then he's stuck selling is house for the same price he bought it; he has no incentive to move. Someone is willing to pay him much more for that house, but they can't. This is what it means for resources to be allocated efficiently, and it depends on the ability of prices to change over time.
Fixing prices also affects investment. For example, if I believed that prices were likely to rise in some area, then I'm incentivized to buy property there, build housing or fix it up, and sell or rent it to capitalize on that price increase. The rising prices bring investment: I might build an apartment building to take advantage of rising rents. By comparison, if I know that my property will be rent controlled, then that limits my financial upside from investment, and removes my incentive to invest, which is also bad for the economy if it would otherwise happen naturally.