It would be lovely
I really have trouble without the thickness search, it is really hard to search for coins especially if they are old and ancient
For ancient coins this would help you even less then for modern ones. The thickness often varies greatly because of the nature of manually hammered coins and the information is almost always missing anyway.

What percent of coins (or non-banknote exonumia) have a thickness listed?
In other words, what percent of matches would be excluded because the information isn't present? (Or does the search include everything without a thickness because it might be a match?)
This feature would be very useful for identifying damaged coins if implemented as the Weight and Size fields. I mean, allow the user to search for a thickness range.
Use case: I have a damaged Macedonian coin that I cannot see many details on. However, I can easily measure it with a caliper or a ruler. If I have the size/diameter, thickness, and weight (for which I can take advantage of the range feature), it becomes pretty easy to spot the coin. Even if I don't know the country, these 3 measures would emilitate thousents coins from the list. And if you have any small pieces for another search criterion, such as some number, text fragment, etc, probably the coin would be almost unique in the search result.
Also, adding the Edge style as a search criterion could be very useful for this use case.
I hope my use case is helpful.
The vast majority of coins in the catalog do not have thickness values so relying on searching a specific thickness range would more than likely eliminate the very coin you're searching for. Before this can be useful the coins in the catalog would have to be populated with their thicknesses which is problematic at best.
Edge style search is being tracked here: https://en.numista.com/forum/topic66736.html
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