I don't think the Free Agency/Salary Cap Era (FA/SC) really makes it more difficult for great teams to maintain dominance. You will sometimes hear "conventional wisdom" that before the FA/SC, great teams were able to hoard their talented players because there was no salary cap and no free agency. This isn't entirely true: the San Francisco 49ers, for example, won five Super Bowls between 1981 and 1994 not because they hoarded the same players, but because they consistently drafted well and added talent to maintain their dominance.
The 49ers won the Super Bowl for the 1981 season. They won the Super Bowl again for the 1984 season. Look at who they drafted between those championships. In the 1982, 1983, and 1984 drafts, they drafted starters on the 1984 championship team like Bubba Paris (T), Roger Craig (RB), and Riki Ellison (LB). They won the Super Bowl for the 1988 season with starters like '83 draft pick Jesse Sapolu (G), '84 draft pick Guy McIntyre (G), '85 draft pick Jerry Rice (WR), '86 draft pick Tom Rathman (FB), '86 draft pick Charles Haley (DE), '86 draft pick Steve Wallace (T), '86 draft pick John Taylor (WR), '86 draft pick Tim McKyer (CB), '86 draft pick Kevin Fagan (DE), '86 draft pick Don Griffin (CB), '87 draft pick Harris Barton (T), and '86 draft pick Larry Roberts (DE). So after winning a championship in the '84 season, the 49ers won another championship in 1988 with 10 starters that they drafted AFTER 1984 (including 8 Super Bowl starters from the 1986 draft--arguably the most successful draft ever). The 49ers won again in 1989 with a similar nucleus. It took a few years, but in 1994 they won again with more new players like CB Eric Davis ('90), Ricky Watters ('91), Merton Hanks ('91), Dana Stubblefield ('93), Bryant Young ('94), William Floyd ('94), and Lee Woodall ('94).
This isn't even a comprehensive, thorough list: I briefly matched Super Bowl starting lineups with the 49ers' Draft History. But this brief look should show clearly that the 49ers didn't merely hoard their talent to win all those Super Bowls. They consistently added talented players in order to maintain dominance, even before the FA/SC era.
Consider this: 1981 championship team and the 1989 championship team shared just two starters (Joe Montana and Ronnie Lott). In a matter of nine seasons, these two championship squads turned over 20 of 22 starters.
Did the 49ers benefit from lack of salary cap and lack of risk of losing players to free agency? Perhaps. But considering they won four championships in nine years by replacing 20 of 22 starters, I doubt they merely hoarded their talented players. The 1994 team played in the FA/SC era, and added key free agents like Deion Sanders and Ken Norton, Jr., so if you'd like, you can even leave them out of the discussion. But between 1981 and 1989, the 49ers maintained long-term success very similarly to how teams maintain long-term success in the FA/SC era: they consistently added quality players to the roster to replace players who either left the team or saw their skills diminish.