Are you suggesting to creat a full wallet node instead of using SPV wallets?
Anytime, yes.
Even when using SPV wallets (like electrum) I would suggest to run your own (electrum-)server (which also requires to run a full node).
And if you're running your own full node + your own SPV-server already, it doesn't take much more to run your own BE too.
Of course most people don't do that and I get why, doesn't change the fact that it's the better choice though,
simply because you don't have to trust anyone.
Because if Blockchain Explorer is not trusted then things will get confusing for everyone. Because it just displays the data of blockchain even the validators and miners are increased so much since the inception of BTC so we should trust the BE.
Sure, the blockexplorer
should just display the data of the blockchain,
but how can you be sure it's showing you the correct data? The operator
could tamper that data in any way s/he wants.
I'm not saying s/he would, but you need to trust them anyway.
I do understand that everyone was running a full node but what I do not understand here is how that provides one information and history of transactional data in live time. Just like the BE do. Because AFAIK, the addition of new transactional data when occurred then that data is also upgraded in all the blockchains (means who have run a full node). But what happened in between that time who knows that live status's information?
You said it yourself,
the BE just displays the blockchain-data in a user-friendly way.
If you already have the blockchain, you already have all the data and what's not yet in the blockchain is waiting for you in the mempool to look for.
Running a full node, you've got all the data there is, no need to ask a third-party for information you already have.
Again, I'm not saying BEs are bad, or noone should use them, or anything like that, I'm using them myself.
But BEs have nothing todo with "trust in BTC".
If someone tells me, s/he send me coins and sends me a link to a BE as "proof", I still don't believe anything s/he says, or the BE shows.
If it's not on my copy of the blockchain, s/he didn't send me anything.
PS: I got those 5BTC from Gavins faucet, but I sent them back a couple of minutes later, just wanted to try if it works.