That's one way to approach it if you don't want privacy-infringing Electrum servers to get certain data from you. But what if some or all of those blockchain explorers are also honeypots that collect, store, and share user data with companies and agencies interested in conducting various kinds of analysis? You will be avoiding one problem but creating another one elsewhere...
They are. Broadcasting transactions generally won't leak privacy more than your SPV wallets. Even if they were to collect data, they would only get as much data as your browser leaks, which in the case of privacy conscious ones, it isn't that much. I would recommend using a privacy-centric browser and using a new identity for each session, which in normal circumstances can't provide sufficient data regardless.
Data from your browser fingerprint may not seem that much, but it's quite valuable on hands of group/government who perform all kinds of data collection to perform data de-anonymization.