Of course in reality no one wants to keep their coin holding keys online so in Alogorand you can authorize a set of "participation keys"[1] that will be used to create blocks on your coin holding key's behalf.
Hopefully you've spotted the problem.
You can send your participation keys to any malicious party with a nice website (see random example [2]) offering you a good return.
Damn it's still Proof-of-SquareSpace!
I believe we are talking about a comparison to PoW, correct? If you want to mine PoW, you need to buy expensive hardware and configure it to work, and wait a long time to get any return by solo mining. Or you can join a mining pool, which might use your hashing power for nefarious purposes.
A mining pool using your hashrate for nefarious purposes can easily be observed since they send you the contents of the block you are mining before your hardware starts working on it. This difference is crucial. Mining pools exist just to reduce income variance.
Or you might skip the hardware all together and fall for some "cloud mining" scheme with a pretty website and a high rate of advertised return. So as you can see, Proof-of-SquareSpace exists in PoW as well!
I'd agree that "cloud mining" pretty much is Proof-of-SquareSpace for PoW. Fortunately these services make up a tiny fraction of hashrate.
The PoS equivalent of buying mining hardware is setting up your own validator and not outsourcing that to anyone else. So both PoW and PoS have the professional/expert way of participating, and the fraud-prone, amateur way of participating. The only difference is, with PoS the professional/expert way is accessible to anyone with a raspberry Pi and a web connection, which is a much lower barrier to entry than PoW.
And yet despite this, the fraud-prone amteur way of participating accounts for the majority of stake in PoS systems while the professional/expert way of participating accounts for the overwhelming majority of hashpower in Bitcoin. It looks like you have elegantly proved my point!
LL