Well, I like the fact that movement costs a die, that gives them missile characters more of a chance to get a shot off before enemies close to melee; I just think shooting an arrow should be roughly on par with swinging a sword. So, if you are sitting there with a bow & arrow, and someone is 30' away, you would have about the same initiative die as he does, plus he would have the movement die. This way you're likely to have a higher initiative, but it is not a sure thing and you have to ask yourself if it is worth it. On the other hand, if he is right next to you, it is an much more up in the air if you could get your shot off before he smacks you.
I agree that closing with impunity is a problem.
I think the real problem is that ranges (proportional to typical table/map sizes...especially when you cut off most of the table with players' books, etc.) and encounter distances are so proportionally small. At least IME, unless the archers have meatshields, they have great difficulty avoiding melee.
I've lately been toying with the idea of adding some kinds of reactions or threatening mechanic for missile attacks, or heck, just a reaction-based initiative system like Two-Hour Wargames. But there are a lot of entanglements with the D&D vs. what THW uses. (Like when two figures engage in melee, they go until one of them drops.)
The basics would be something like:
ready means: not surprised, aware of other units, and hasn't acted yet this round.
1: Units who are ready* and wish to act first roll for initiative, highest becomes active.
2: Active unit either take an action or move until interrupted.
3: Interrupting movement: when an actor moves into LOS of a ready unit, it may move up to an additional 10'. The sighting unit may then make a ranged attack, if it still has LOS. Similarly, if the sighting unit is less than 15' away from the acting unit. The Sighting unit may move to engage the active unit. Interrupting the active unit this way costs the sighting unit its action.
4: The active unit may continues to finish its movement and actions. This may provoke OAs from units that engaged it, if they still have a reaction.
5: If there are still ready units, GOTO step one. (Maybe have units that still have move or bonus actions do a cleanup phase?)
6: Is combat still happening? If not, new round! (makes everyone ready, again.)
I dunno. Just spit-balling.