Q: Why do all of the landlords in this town insist on a written lease?
A: Let's explore why you might want a written lease as opposed to an oral lease.
Unless there is a provision in the lease permitting early termination by giving written notice, the landlord must let you remain for the full term, provided of course that the provisions of the lease are not broken by you. On the other hand, if the landlord does not live up to the terms of the lease, you have enforceable rights against him or her.
If the lease is oral and rent is paid monthly, the lease is normally classified as month-to-month. Such an arrangement means that notice to you to vacate the premises is binding as long as it is given more than ten days before the next rent payment is due. Thus you might find yourself having to find a new place and move with not much more then ten days to do so. Of course that means that once you move in, the landlord can change the terms of the oral lease, including raising the rent, and force you to either comply or have ten days or so to find a new place to live.
A written lease will also cover many contentious issues, setting out in black and white such things as the number of people allowed to stay, pets, yard care, or even who is responsible for replacing light bulbs and toilet paper.
If you are concerned about being stuck for the entire term of the lease, then often a provision can be inserted into the lease to permit early termination by giving notice, but usually some type of penalty is also established for the right to do so.
A second way to leave, even though the lease has not ended, should be used with caution. Our courts are not only courts of law but also courts of equity. There is an equitable concept called "mitigation of damages". Courts do want to uphold the terms of a contract (which in reality is what a lease is), but it might not be fair to permit the landlord to sit back and collect rent just because someone signed on the dotted line. Thus the landlord, at least in theory, has a reasonable duty to rerent the premises. Often one month is held to be the time that a landlord needs to do so. The tenant then will not be responsible for the remaining time on the lease.
At least in Northern Colorado I have had mixed success. Some judges refuse to recognize these "equitable principles". Others require some reason to apply the principals such as death, or a forced move because of a new job. Still other judges (so-called pro-tenants judges) are more willing to come down on the side of the tenants, and use this equitable rule.
Oops, I am almost out of space. One final thought. Leases vary greatly from pro-landlord to pro-tenant. Buy a pro-tenant lease and then use it to compare the lease proffered to you by your "future" landlord. At least you can compare the two and see which provisions to strike or to modify.
Thus my advice is to go for the safety of the lease as opposed to the freedom of the handshake.