There is no possible benefit to the owner to do more than 1 or 2 years, EVER! As others have said...a lease is not going to keep a tenant in place. It's just a piece of paper - a piece of paper they likely have not thoroughly read and couldn't understand if they did.
What advantage could you have by making it 3-4-5-6-27 years long? If they want to stay after 2 years keep at it one year at a time. If they still like you, and you still like them, no problem. If they hate you or the property, or you hate them, a piece of paper will do nothing to solve that problem. I can't possibly understand why you would give somebody a discount for a multi year lease - rent goes up yearly, that's called inflation.
Additionally, both you and they do not know what their life circumstances will be in 3+ years. What income will they be making? Where will they want to live? Do they have a new boyfriend/girlfriend? Again, this lease will not even be a thought when the tenant is reevaluating whether they want to stay or not 3 years later.
Month to month leases are just as ignorant. If a tenant likes your house, they want to feel comfortable that they won't have to move for at least a year, and most leases give the option to renew if you haven't broken any rules. This makes them comfortable that they will be able to stay in your house as long as they want to so long as they follow the rules. A tenant on a month to month knows their landlord can get rid of them on a whim, with very little notice, and they don't like that. It only advantages the landlord and tenants aren't so stupid they don't know this. People who want to be comfortable in not moving their home again anytime soon will not choose yours.
Month to month again doesn't advantage the landlord much either. If they haven't done anything wrong, then why do you need to get rid of them in a hurry? If they have done something wrong, then it should be straight forward getting rid of them for breach of contract. Sounds more like an overly nit picky/slumlord type landlord strategy to me.
1 or 2 years is enough time for a new tenant to get comfortable in a house, to make it their "home", and decide whether it's time to move again at the end of their term. 30 days is not enough time to decide this, it's not enough time to get to know your tenants, and it's generally not enough for them to find another place if they have to be out within 30 days. Basically don't act like a king on his throne and tenants won't treat you like that. (And when I say that, I mean they will do the opposite of treating you like a king. Don't give them reasons to hate you from day 1!)