With a computer/laptop, you at least have the (reasonable) option to use a full node. If you only have access to a mobile device, you likely are not going to have the ability to use run a full node.
Yes, that is true, but also the more than 400 gigabyte needed to download full blockchain makes most people not to use full client unless they extremely need privacy. While the pruned node have its own disadvantages. So most people have computers but yet using SPV wallets.
It is tricky to use electrum on a mobile device in a way that guarantees your privacy. I don't think current implementations of electrum would make this very easy.
It depends on know the person knows how to use Electrum to still maintain privacy to some extent. The best is to run full node using Tor.
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Like I explained above, you can still maintain privacy to some extent on Electrum, but it is not convenient. It will required two or more wallets and require rerouting Tor connection to each wallet. It depends on the way you are doing it, only different wallet addresses are not linked the way I explained it.
If you will have to use the same wallet, anonymity will be more possible, not privacy.