I don't think this will be a problem, balance-wise, but that doesn't mean it's necessarily good for your players, either.
Most paragon paths with prerequisites tend to have features or powers which modify or require features that are related to those prerequisites.
Cleric paragon paths modify healing word; Ranger paragon paths modify hunter's quarry; Sainted General modifies Divine Challenge, Inspiring Word, and the F11 requires paladin or warlord powers; Daggermaster only works on rogue powers, Student of Caiphon on warlock powers.
Very few epic destinies have specific features required, and those that do heavily modify that feature, so, without that feature, those epic destinies would be pretty bad. Examples include Sovereign Beast which makes your Wild Shape Large sized, and Beastlord, which provides multiple bonuses specific to beastmaster ranger animal companions.
Deva's racial ED, Soul of the World would have to be disallowed or it would automatically be the best possible choice for almost any character, but most racial destinies offer stat bumps similar to the base racial bonuses, and modify that race's racial power.
In my experience, option paralysis is a more common source of party optimization disparity than munchkinry.
For every Paragon Path like Stormwarden that could be great for any STR/DEX class there's ~10 that have at least one feature or power that would simply do nothing if you lacked the proper class, so for the most part, all this does is increase option bloat.
Additionally, most paragon paths and epic destiny prerequisites can already be met by multiclassing.
If a fighter wants to take Darkstrider or Blade Dancer, all he has to do is take a Ranger MC feat, and then he qualifies. Way less than 10% of all paragon paths have a specific feature required. Some of those are powerful, like Battlefield Archer, but the Archer Ranger is the best Archer archetype striker anyway (and it has both a feature and a power which modify quarry), so who else would want it?
There's a slew of epic destinies with no (or minimal) requirements, and the more requirements they have, the more likely they are to match the specific mechanics of a character likely to meet them. Arcane EDs have implement powers and mental stat boosts, martial EDs have weapon powers.