I can't tell you WHY 53 is the limit, but I CAN tell that it hasn't always been 53:
Another reason why K-Ps might have died out in the late 1970’s was the increased roster size, allowing for more specialists. From 1964-73, rosters were limited to 40 players (hence the Vikings’ old “40 for 60" motto), but increased to 47 in 1974 (maybe an effect of the player strike?). The active roster limit went to 43 in 1975-77, 45 in 1978-81, 49 in 1982-1984, and has been at (essentially) 45 since.
:: Travis — 9/22/2006 @ 11:41 am
http://www.footballoutsiders.com/2006/09/22/ramblings/too-deep-zone/4271/
Dear Mr. Remmel: how has the NFL roster limit changed? I know when they instituted free substitution in 1950 teams had something like 35 players on a team. When did that go up? When did it get to the 53 that it is today? Thank you for your time. - Zac, Oshkosh
Dear Zac: the roster limit's growth has been a relatively gradual thing, beginning with the first such limit, 16, in 1925. That number, by the way, increased to 18 players in 1926, remaining static for three years. For further example, the limit was increased to 40 in 1964 and remained at 40 for nine years, through 1973.
More recently, the limit has held firm at 45 active players annually for the past 16 years (1991-2007). Each team also has a list of eight inactive players for each regular season and postseason game. Also, provided that a club has two quarterbacks on its 45-player Active List, a third quarterback from its Active List is permitted to dress for the game, but if he enters the game during the first three quarters, the other quarterbacks are thereafter prohibited from playing. Teams also are permitted to establish practice squads of up to eight players who are eligible to participate in practice, but these players must remain free agents and are eligible to sign with any other team in the league.
http://www.packers.com/news/stories/2007/11/06/2/