I look at designs like that and think ‘Why?’
Too much wasted space – those lids could be much thinner.
How simple would it be to include a tool to remove the die from its space – a magnet on a stick? Bigger-thread ones are easy to pick with fingers, smaller ones may be more difficult. I can already hear the comment that “I’ve never had a problem getting them out”. A piece of bent wire might even be enough.
Colour coded would greatly assist in selecting the right thread form.
Timber boxes need to be kept dry (and metal ones kept warm?) to avoid moisture problems, or to be given a suitable soaking in an anti-rust medium (oil?) to help preseve the dies over the years.
Nearly all my tap and die boxes have two closing clasps – I suppose it might be considered ‘overkill’ but it does help prevent warpage.
Ply might be a better choice – although it is a lot harder on cheap Forstner cutters.
I prefer the dies to be proud of the holes in which they sit. A routed lid with an oily cloth affixed seems to be an alternative without too much extra work entailed.
A good idea to put them in separate boxes, though.