Why would slow healing mean the mounters take the dodge action? They're still only going to exist for that one combat. It's not like they're going to be punished with a boring convalescence period if they take too much damage.
To slow down the progress of melee characters or to prevent them from reaching their ranged and or bosses.
It works both ways.
Take a standard group, 3rd level encountering 6 hobgoblins in a room. The hobgoblins win the initiative.
Two goes to the door and block it. Both dodges.
4 start shooting at back ranked characters or even melee characters depending on the situation.
Now it is the character's turn. The back ranked character may try to shoot the archer, but the front line ones must get rid of the dodgers. Easier said than done. At AC 18, and dodging these hobgoblins now have an AC equivalent to 23. One of the front rank can use the help action to give the other one a normal chance to attack an AC 18 which is not that easy for 3rd level characters.
Expand a bit more. Use of Orogs. Characters are now level 6 or 7.
Same AC. Same situation. But now instead of dodging, the two front line orogs now grapple one of the front liners and simply put him behind them. (If they succeed). One of the grapplers will also drop down with the players, prone. Now one of the front liner is surrounded by 6 angry orogs, four of which will attack our grappled character with advantage... And if a pit is near, the grapplers might decide to show the grappled one how deep is the pit... Grappling is especially hard for casters and they want to avoid it as much as possible. Remember that spells with somatic component requires a free hand, which grapplers do not have. This restricts casting to Verbal spells only of which there are not many...
For the character's side.
Characters can benefit from the dodge action because it reduces the amount of hit they can take.
When you do not recover full HP on rest, you must spend HD to heal. These are a finite resource.
Yes, a healer can heal. Be it a bard, druid, or cleric but doing so makes it that they do not use their spell for other things.
If then, healing is a finite resource, and you recover only half of your HD per days of rest, you want to lose as few as possible and to maximize both defense and damage potential. As if you have to spend more than half your HD on a given day, it might mean that you will start with less than full HD the next one. This can lead to a death spiral as you have less and less resources to "press on".
Since players know that most intelligent foes will do their utmost to prevent the whack a mole, as soon as they get lower than 50%, they start to dodge, why? To prevent being hit too often allowing the healer to heal them back up if necessary or to allow other to finish the enemy with ranged attacks. Otherwise, they know that each hit would reduce both their HP and their HD resource. Cantrip and ranged attacks are really useful as are summons and others to mitigate and dish out damage. Characters will use shove, push and any other ways at their disposal to break enemy formation or allow friends to get advantage on their attacks. A rogue with advantage on the attack is deadly. Especially if a Battlemaster is there to "order" him to attack again on his turn (allowing a second sneak attack with advantage).
Yes, attack is the best defense. But when you know that after that you might gimp yourself for the next fight and the next, you start thinking about ways to extend your resources. Faced with enemies that tries to survive and "win" you have to adapt and do the same. This means that an all attack stance at all times is doomed to failure in the long term.