So, maybe the typical closer can go 1 IP in half the games, tops. That's 81 IP in 81 appearances, which is more than almost all closers give. Many games, they are not needed. Other times, you need them 4-5 games in a row, but they can only give you 3 out or 4 of 5.
A two inning guy that can give you 2 innings twice every 5 games would be giving you 4 IP every 5 games or 145 IP/season. He may be brought in in the 5th or 6th inning and maybe not finish (close), of he could be used for the 8th and 9th.
I think the two inning guy, even if they can only go 4 IP every 6 games gives you 108 IP a year, and you can plan on his usage more than with a typical closer.