setting aside that blockstream products/services are great, that particular example you're using their node (and satellite network), not your own

when you're not using your own node to broadcast transactions, you're relying on someone elses node and trusting them not to be malicious to do it on your behalf. it may seem tinfoil hat-ty, but malicious nodes can get pretty creative, they could set conditions on broadcasting your transaction, track your tx with queries on block explorers to create a profile on what utxos belong to you even if you go to multiple cafes, or just simply witholding broadcasting your tx indefinitely with no recourse. it's not unheard of, better to run a node 👍

blockstream products and services might be great in a pinch (and of public infrastructure they're probably the best) but it is no substitute for running a node they even say so themselves. related to also why it's not advisable to use random electrum nodes too