There are a couple of different aspects in "writing a will on a blockchain".

1. Your will: Normally this is some kind of paper you write, stating your will who should inherit what, right?
   So this could be a smart-contract on Ethereum or other smart contract able chains.
   One issue with smart contracts (at least at the moment) is, you actually cannot change them...as they are on the chain and that means distributed to 1,000s of nodes, a change is not possible.
   So - if you make up your mind about a person in your will (or want to add someone) or any other aspect (donating your house, or car or whatever) - you need to have a solution to clearly cancel that first smart contract and add a new one...
   So while it is possible, you would have to be careful with it.

2. Money: If you are "just" referring to whom to pass on your money - yes, then you probably just need to ensure, those you have chosen get your private keys - but how seems really complicated.
   In contrast to our banks, no one would e.g. be able to check if your lawyer, whom you handed your keys, will give them to those you specified. He could just use them himself...
   And as the private key is nothing you want to place on any network, I (for now) see no solution using a net driven service/solution....as it would be a great risk placing it somewhere on the net.

But I like the idea - not sure, how to do it, but yes - it is an "easy" contract (as it is "just" your will and not a 2nd party involved).
But thinking of it - how would a contract know for sure, you are dead?
There would have to be some chain based institution verifying that, no?

Thanks for the mind-game!