First glance, the concept is a bit meh.
First issue is why for a free process do we have to go to an NPC to do this process, just seems like an unnecessary pre-req when they could of just given us an ability to use.
Second they could of added a "payment" via shards, since each materia is attuned to a color:
Attributes=Ice
"element" materia=it's element
Heaven/Savage=Fire
Battledance=earth
Gather=Wind
Craft=Water
Quick=Lightning.
Say you want to combine 2 gather, 2 craft and 1 quick all grade I, you put them in the slots and it would say "This process will require 20 wind shards, 20 water shards and 10 lightning shards to proceed"
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Third is an unknown issue atm but the process should allow for 5 of the same exact materia to go up a grade regardless. So if you mix 5 Strength I materia it should turn into an STR II materia, 5 STR II materia into STR III and 5 STR III into 1 STR IV.
In the process of combining I and II and the likes the % chance of getting upgraded version would be based on the amount of highest tier you are using, So say you use 2 STR II and 3 STR I then you would have a 40% chance of getting an STR III, if you do 3 DTR II 60% 4 STR II 80% and of course if you use all 5 as STR II then it would be a 100% chance of STR III.
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To be honest this "transmutation" concept could of been a lot more open in a sense, as I think more on it they could of allowed materia duplication via crystal/cluster cost.
So in the above process you pay those amount of shards to attempt the transmutation.
The Duplication process would work something like,
If you want to duplicate the STR I you would need to use 100 ice shards.
STR II 100 ice shards 50 ice crystals
STR III 100 ice crystals
STR IV 50 ice clusters 50 ice crystals
The above would be a means to eliminate surplus shards on the market and the process itself could be % based. For tier 1 duplication it would be 80%, tier 2 80% tier 3 40% and tier 4 20% success rate.
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With the above the idea is different routes to get the the same destination. If you want to burn 5 materia for the chance of a new one you can pay less shards to attempt it but of course you lose 5 to gain 1 new one but if you use the same exact materia of 1 type then you are guaranteed that upgrade(which may be possible haven't tested yet).
The idea in it's current implementation feels half-baked it doesn't really revitalize the materia market because it doesn't add any potential use towards the best gear in the game. This process feels like it could/may help out craft/gathers more and is moreso a process used to encourage players to materia their low level gear rather than using it and never getting rid of it.
It may work for some and they may eliminate a good bit of materia from the market as people test it out, but it does feel like once the rush of "interest" disappears from this new concept the flood of materia will just re-enter the market since like others have commented you increase your odds of better materia when you attune it to the gear you later turn into materia, so why waste 5 materia for the chance of 1 when you can just those 5 on a piece of gear and increase your odds of gaining a new materia that way.