Guaranteeing each team a possession is, IMO, an awkward blend of the college and pro OT systems. It has the unfortunate gimmicky quality of the college system, but not it's madcap shoot-out style appeal.
But what's worse is that you're not exactly solving any problem. You still have, in many cases, the issue of one team getting the first shot at sudden death.
Let's say team A gets the ball at the start of OT, picks up a first down or two, but gets stopped in long FG range. They can try for the FG, but without the benefit of sudden death -- even if they make it, the other team gets a possession. If they go for it and miss, however, they're giving Team B the ball, already almost in FG range... but now, Team B gets the advantage of sudden death. Why is this any fairer than Team A getting the advantage of sudden death, first?
Some would argue "Hey, Team A had the ball... if they didn't want to get sudden deathed, they should have scored." The same argument applies to standard sudden death overtime -- "If they didn't want to get beaten on the first possession, they shouldn't have let the opponent drive into FG range."