No, it's not.
If I understood you, this begins with the assumption that theymos generates all the keys. If in some way his procedure is compromised, all funds can be stolen regardless of how well everyone else did. If theymos chooses to embezzle (or to just force a dictatorship), he could keep a copy of the keys and steal the funds whenever he wants.
If we do assume the issuer is a benevolent, we don't need the complex cryptography - everyone can just tell the leader what they want and he will do the right thing.
If theymos deletes the keys himself, then it is decentralized and ability to spend will be based upon fractional collusion.
If we need to rely on theymos to delete the keys (
and that the keys weren't somehow compromised during his generation process), then it's not decentralized.
Issuer risk can be greatly reduced if you use multisig (each party bringing their own key) instead of secret sharing. The issuer's role can then be reduced to compiling the list of keys without each member knowing which key is whose.
Also: With the method as described, huge risk of loss. If each person has 1% chance of loss, the average loss with "normal" storage is 1%. With your method average loss is 4%.
Loss can be mitigated by reducing the fragmentation of a key; for instance, halving the number of coins in each wallet and fragmenting the key to 2 fragments.
The nice thing is that you need a minimum collusion number of 4 in order to even possibly be able to spend any of the coins as I had implemented. I guess it's a tradeoff.
It's also guaranteed that with 100% of the currency will be spendable upon the agreement of all key fragment holders, too.
You can greatly reduce loss risk, without reducing the collusion factor, by having 4 groups of 4-of-5 rather than 5 groups of 4-of-4, etc.
Also: Your method as described has a lot of variance. (7-way collusion gives access to X coins on average, but on practice it can deviate significantly from average). You can reduce variance by having more wallets, with overlap in custodians (e.g., each member is part of 10 different 4-of-5 groups, total of 40 wallets).
With combinations of wallets of different group sizes, you can control the correspondence between number of colluders and number of coins that can be spent.
Anyway this is getting completely orthogonal to the original purpose of securing funds.