The simple answer is that the classes define themselves by their class perks and abilities now, more than by passive benefits to base mechanics - so, while, yes, a wizard with 14 dex and the weapon master feat giving them access to a long bow has the same basic ability to hit and deal damage with that bow as a fighter with 14 dex does... the fighter has, or has access to, many and various elements that enhance their ability to do this - fighting styles, feats and other class abilities that, for example, give them a flat bonus to hitting or damage with certain weapons, extra attacks, the ability to ignore or reduce cover for their targets, and so on. Even without any extra feats, the Wizard at level 5 can make one shot with their bow, at base calculation, while the fighter at level five who chose archery as her fighting style can make up to four shots on a single turn with that same bow, and have a higher bonus to hit with it.
In terms of feats: After 6th level, until level 16, fighters functionally get a feat every 2 class levels instead of every 4 (so at 6, 10 and 14, as well as the normal ones at 8, 14 and 16), for a total of 3 additional feats on top of the 5 everyone potentially gets - these can be used to increase your ability scores as well, so fighters in particular have an easier time capping out the ability scores they want to, without sacrificing flexibility.
