Earlier quoted context omitted.
Lighntning, also known as not-Bitcoin. Lightning does away with Bitcoin's guarantees, unless you close the channel after each transaction, at which point it costs more than sending BTC directly. And something like CashApp is even worse - it only uses BTC as a way to circumvent banking regulations, and for name recognition. Otherwise, it could just as easily work on top of regular banking, or do away with BTC entirely…
This first paragraph is simply untrue. You are always holding a valid signature to spend the latest funds. The additional assumption vs simply holding your own funds is a throughput requirement: that miners not censor your transactions for some (up-front-chosen) period of time. With normal funds there is a non-censoring requirement, but it's more vague since the miners may have to censor you forever to make your fund…
And related to censorship, I'm not sure what is the point you are trying to make. Still, censoring forever is not hard (you just add some wallet address in a list, and look those up before choosing which transactions to include in a block), and is completely equivalent to how payments censorship works in regular banks as well.