. You say "I don't understand why anyone.....". Well, that's when people just want to stay in Thailand a bit longer than they have a visa or visa exempt entry and many times cannot fulfill the requirements to get e.g. a year extension. So they 'border bounce' (go out and in again to get (till 31 of march) 45 days visa exempt, or do a 'border run' to get e.g. a new touristvisa at a Thai Embassy/Consulate in another country. With both options you can extend with 30 days in Thailand. Also some people have e.g. a multi entry visa non imm. O, with that you can stay in Thailand for 90 days. Each time you do a 'border bounce' you again get 90 days of stay. This for a year until the visa is void. Multi entry Tourisvisa the same procedure but with 60 days for a half year.
2 Friends of my, could also do this IN Thailand. 1 Dutch and 1 Austrian. Really don't know exact what papers they needed but original legalized and translated to Thai and again legalized that one for sure.
. So some people use this visa for staying almost 15 months. If you plan it a bit, and you come back just before the visa expires, you get another 90 days ! But for you not relevant I guess.
You also can ask for a Non imm. O MULTIPLE Entry in your home country. Then you need only one border bounce to get another 90 days. (Visa is valid for 1 year and every time when you leave and come back you get 90 days as long as your visa is valid)
If you have enough money in your Thai bank account (800k฿ 2 months before you ask the year extension) it's ofcourse possible to get a year extension. Maybe also ask a re-entry permit then, should you come back within that year.
I think it is wise to legalize your American marriage in Thailand too when you are here. This for future use ? ('Only' 400k฿ in your bank account needed or 12x 40k฿ per month as international transfer instead of 65k฿ per month
There IS a form which normaly will be accepted by many imm. offices for a home country insurance. But...I hear/read that that form is difficult to get it signed by your home insurance company. Maybe give it a try ? (See form at my own answer)