Personaly, I think that melee combat is lagging a bit behind ranged combat. But not by much.
Here is few suggestions to help it along.
1. Raise the damage die of non-finesse melee weapons by one die. 1d4->1d6,1d6->1d8,1d8->1d10,1d10->2d6,1d12/2d6->2d8.
2. Making ranged attack provokes Attack of Opportunity(AoO) in addition of suffering disadvantage ot attack roll.
3. AoO does not use reaction. Reaction should be used of special class abilities not a simple swing. You have a number of AoOs per round equal to your proficiency bonus.
4. Ready action can be used to make every attack as normal Attack action. That way when archer peek around corner to shoot you can make your "full attack" on him.
5. Count the damn ammunition and check for load. Archers cannot pass whole campaign with starting 30 arrows and they sure can't carry 500 arrows around without magic quivers/bags of holding.
6. Add charge action: Action, add half your speed to your movement this round, but all movement must be in a straight line. If you move atleast 20ft make one melee attack as bonus action.
7. Add new feat: combat reflexes: +1 to str, dex or con. You have advantage on AoO attack roll, and deal max damage with AoO.
8. Add Run action: After you use your action to Dash, you can use bonus action to Run. Add your base move speed to your total speed for this round(with Dash, total of 3× speed). You can only move in a straight line.
I agree with #5 and #6, and a variation of #2. But not for your reasons.
Archers were deadly. Ranged attacks (preferably from behind cover) should be a go-to tactic for just about anybody. The #1 reason why? Because you can't get killed if they can't hit you.
But, you need ammo, and I don't see any reasonable explanation as to why charging requires a feat. Hold your spear down and run at the other guy.
For #2, I think it's trying to target somebody else when there is somebody next to you with a sword is stupid. Opportunity attack, absolutely. And if that hits, it ruins your shot. In fact, I might go so far as AoO with advantage.
No to #1. If anything I'd do the opposite. Bowhunters are looking for a 1 shot kill, whether it's a deer, a bear, lion, whatever. Humans are much easier (although armor was effective, past short range anyway).
No to #3. The economy of actions works really well in this edition. I wouldn't change that.
No to #4, either. For the same reason, you're taking time to not do something. But a ready action would negate any bonus the archer had for being hidden.
No to #7. At least in part. Advantage + max damage is too much.
As for #8, I'm certainly not opposed to additional move amounts. However, in my campaign we use AD&D-style 1 minute rounds. A normal person can move 120 feet in a round without running, and much more if they sprint. To put it another way, I usually don't worry about how far somebody can move in a round, it's almost always irrelevant.
Running across a field towards some archers. That's a different story. The longer you're in range and not within melee closing range is a dangerous proposition.