There's more.
Mike, many guys have done their first flights just fine and you probably will too...buuut many of them have also busted their a$$e$, the reason that the NTSB, FAA and EAA came up with the LODA for CFI's.
As a CFI, we teach by the "building block" system, whereby each maneuver you learn is based on another maneuver previously learned, even if it was learned in a car. e.g. going uphill takes more throttle to maintain the same speed....same thing applies to airplanes...there is a method to the madness
We don't teach forced landings until you've mastered speed control in a glide, or we'd be putting the cart before the horse.
We also quickly learn a student's shortcomings and then work more on those sections in the learning curve.
We are few in number, as you mention..the FAA makes getting a LODA a pain, unlike the first five years that the EAA administered the program.
Secondly, the additional insurance has turned us away as well. Furthermore, it's hard on an airplane. I had my -6A rudder bottomed out twice, crosswind landings sideways because the guy has forgotten how to do them, or he's spent all his time and money building, not flying.
Get current before your first flight in something with light controls, like a C-150 and do crosswind landings the
RIGHT way before your first flight.
Good luck,