You'd pretty much do exactly the opposite thing by trying to check your privacy through block explorers. The thing is, it's quite hard to keep your BTC unlinked to your identity (or at least to sufficient information to connect the dots) all the time without mistakenly leaking crucial data about your devices and location.
Having your privacy up as close to 100% as possible would mean absolutely nothing if, by clicking the wrong button, you mistakenly open up a block explorer with a transaction of yours. As the ledger is transparent, one little mistake would make your entire privacy on the blockchain poof in no time -
and be written in the ledger forever out there.
Take it another way: imagine you have a very important text from history that has a coded word in it nobody ever understood. Finding what exactly the codename was means uncovering the entire text and understanding it all. Same goes for your Bitcoins' path. Finding the smallest information about you (IP, orders, exchange accounts, browser fingerprint - anything) means possibly uncovering your entire history.
If you want maximum privacy, the average Joe would most likely have to first of all reconsider the OS they're using cryptocurrencies with. Install a FOSS Linux distro, go through a few CoinJoins (or mixers), throw your balance from one address to another a few dozen times to try erasing the mixed history (some people do have a problem with them) and, finally, move it all to a fresh Tails OS Electrum wallet and only use that one from that point on. From time to time, it may not be a bad idea at all to throw your balance again in a mixer (or CoinJoin) just to make sure you continue making your BTC path a pain in the arse for anyone who's willing to go after it. Tails OS has system-wide Tor active, which drastically improves your privacy.
Word of advice, if you're going to use block explorers, at the very least at least use Tor browser when doing so for better privacy. Not sure if blockchain.com works well on Tor(I assume there would be a crap ton of traffic lights and buses involved), but Blockstream's explorer does work well on Tor.
Turning JavaScript (press the shield in the upper-right corner of the browser and modify security level to Safest) off is even better. It does mess up with most websites though.