I totally agree... In general I don't mind overlapping skills, but the climb and disguise cases are more like having skills(tools) that are entirely contained in other skills. They make little sense unless the tools unlock additional benefits. They can easily trick a player, especially a beginner, into picking both the skill and the tool, only to find out later that he has been deceived.
I'd go with a different approach - one which I think has support in the playtest (the wording is unclear in a number of cases (... okay, most cases), but I believe it's been clarified on twitter/L&L - I'll see if I can dig up a reference later). I don't think there's a real overlap here; each tool should provide you with something that you *Cannot* get with the skill alone.
Looking at tools in the playtest:
Artisan's Tools: Clearly distinct from skills
Climber's Kit: This is the one that needs better descriptions more than any other, I think. I believe it's also the one that had some clarification. Hopefully the full rules will come with a clear, concise description of what the kit gives you.
Disguise Kit: While it may appear to overlap with Deception, the key difference with this is that you can prepare a disguise ahead of time, possibly getting someone to help you (to provide advantage) or taking 20 (if that appears in the 5e rules). Once you've made that check, it stays with you until the disguise is removed. If you don't have a disguise kit, then you have to use your deception skill every time you interact.
Healer's Kit: ... This one's really distinct - could be clearer, but I'd be happy if all the tools looked like this:
Using the Medicine skill, you can:
* Stabilise a dying character with a skill check
* Diagnose the (common) illnesses affecting someone
Anyone with a Healer's Kit, whether they have proficiency or not, can expend one use of it as an action to stabilise a dying creature without a skill check.
With proficiency, you can use it with the Medicine skill to administer "other sorts of first aid". That would presumably include treating the illnesses you can diagnose with the Medicine skill.
Herbalism Kit: Clearly distinct from skills
Musical Instrument: Clearly distinct from skills. Even if the "instrument" is "Oration"
Navigator's Tools: Another one that needs to be cleared up. I've been ruling that with these, you can automatically know which way is North and can use checks to precisely determine other factors such as how far North or South you are of a known point. Without these tools, I allow Wisdom[Survival] checks to work out where North is and to estimate your location from a map or prior knowledge.
Poisoner's Kit: Clearly distinct
Thieves' Tools: Clearly distinct
Basically, there's a lot of separation already. I just think they should clear up the descriptions and provide better examples so that a tool will always allow you to do something over a skill alone.