I think that your suggestion certainly has merit. The rep bar seems too high, and the tag-specific part could possibly be rethought.
It still isn't something entirely trivial, so I thing that there should be some reputation bar. This is the official position too. The tag system is more complicated than it seems at first glance. And creating synonyms is a dangerous action, because it not only results in a tag no longer being available to use, but also in the system actively changing user input without oversight.
The users who can do this should have a good idea of what are good tags vs. bad tags (e.g. that we don't want meta-tags), should know that synonymization has potential destructive effects, and above all, should be aware of how both tags are used on the site (or know how to check it).
An imaginary example: we could have had a long-standing tradition of using the consistency to indicate problems with a recipe turning out inconsistently well, so sometimes working and sometimes not. This wouldn't be an ideal situation, and may need some thought of how to change the tag taxonomy for this concept, but a synonymization with texture on purely linguistic grounds would have been the wrong approach, and would have seriously complicated the situation if implemented.
The whole problem may be worse on other sites such as Stack Overflow, where many users are active only within certain tags - because a C# programmer doesn't generally answer R questions - and may be entirely unaware of niche meanings of terms used in a tag. This is probably the rationale behind requiring the reputation to be reached within the tag rather than total site rep.
From my point of view, the current situation is still suboptimal. On most sites, tags don't compartmentalize the usership as much, and people don't get very high reputation in a single tag. Also, we hope to catch such issues before the tag becomes so large that people amass thousands of rep points in it! So, I could imagine a better privilege trigger to be a lower reputation, and/or to being about total instead of tag-specific reputation, and/or having a more complicated condition such as being an active editor or active in retagging.
That being said, this is a low-impact request. On Cooking, we have a total of 97 synonyms created in all our history (14 years), but only 7 in the past 5 years. Three of the seven were part of a single cleanup. Also, as this example shows, we tend to only do synonyms after a discussion on Meta, since there are very few examples where it can be done without dangers lurking. In practice, anything beyond a simple pluralization (tomato -> tomatoes) probably merits a Meta discussion, just to have more eyeballs looking out for unintended consequences.
Still, I can see the reasoning about changing the threshold, and if the company wants to make the change, I would support them.
