Its the same reason why things like the Climber's Kit, Crowbar, Fishing Tackle, Healer's Kit, and the like are listed under Equipment and not Tools-- anyone can use those things whether or not they are trained.
Honestly, if the idea has legs, then I think adding crowbar as a tool proficiency makes sense too. One of the play test drafts had a "Break stuff" skill, and (on exactly this analogy) a crowbar proficiency could be used to adjust the DC.
There's no rolls associated with Climber's kits or fishing tackle, and even the healer's kit, and so they're not really analogous -- there's no unproblematic way to map improving the use of such items with the proficiency boys. But certainly if someone were proficient in fishing tackle, I'd let them catch a bigger fish, or whatever -- but that's not what the heart of this proposal.
Crowbar is analogous, though. The question becomes whether sliding the DC is more valuable thatn other tool proficiencies.
I agree with pretty much all of this except one thing: making the strength DC higher. Being able to tie cool knots in the rope isn't making the rope itself any stronger, and a DC17 is actually pretty high for 5E, falling between medium and hard. An average human would have a 3/20 chance of being able to break out, not exactly an easy thing to do.
On the contrary, it's way too high for my taste. How often would a tied up character get to roll? Once a minute? Even if it's just a single roll (and other threads recently have shown that's not the way a vast majority of groups play it), that's still a very high escape rate, and why I think introducing a tool proficiency makes sense.
The question becomes, can one become better at tying someone up? I'm suggesting yes, and that the tool proficiency operates at a suitable granularity for those who would want this.
(As for the use of Str rather than Dex -- I'm accepting the rope rules as is; just trying to tweak the tool rules to replicate something from a previous edition. And because I wouldn't trust rope in this game for anything, with the DC set where it's at.).