Tranditionally any computer was able to send and receive email, without much effort. And with the advent of the Internet, computers became connected and email started to work globally.
"Without much effort" is sort of a joke. Until the early 90s, any computer capable of using e-mail was by definition a large machine, administered by professionals. There were no "personal" computers with network connections, with very rare exceptions. There were BBNs that people dialed into, but that wasn't really e-mail, more of a chat or forum site. E-mail was heavily used since the early 70s: until the mid 90s, IBM's internal VNET had more e-mail than the Internet. I started using e-mail in 1982. To hruodr's comment that 1-day delays were normal: No, even in the 80s delays of 10 minutes or at most an hour were expected for sites that were permanently connected; only uucp sites and hobbyists on BBNs had longer delays.
Even in those days, there was a clear distinction between a computer that transmitted and stored e-mail (typically a mainframe or minicomputer), and the device that the end user needed to view or write e-mails (until the 90s that was a terminal, like a VT100 or 3277; later it was a personal computer like a TRS-80 or IBM PC). The important part was that the mail remained on the server. In the 80s, I either drove to the office or lab to use e-mail, and later I had a Hazeltine or VT100 at home, with a modem.
That is when shops like Yahoo etc. jumped in and offered a delegated email service, based on web pages.
Beginning in the early 90s, the Internet (and by that I mean the TCP-IP based heir to the ARPAnet) reached consumers, who started browsing. Since using telnet to dial into a shell machine to read the e-mail there was considered too difficult, lots of web-based e-mail services sprang up; I think Hotmail and AOL may have been even earlier than Yahoo.
And then, in the 90s, individuals suddenly had full-fledged computers at home, with network connections. A whole bunch of hobbyists (including me) decided it would be a good idea to have their own e-mail hosts, and run MTAs, and store e-mail. In the early days of Internet protocols, that was easy enough, but it was immediately open to all manners of abuse.
It is important to understand that web pages (HTTP/HTML) and email (SMTP) have nothing at all to do with each other, ...
No, it's much more complicated than that. To begin with, HTML is an information rendering language. I can transport an e-mail (by any protocol capable of transporting mail, be it SMTP, RSCS, or IMAP) independent of what information the e-mail contains. It can be clear text, it can be HTML encoded, it can be a binary file like a JPG. So yes, HTML and mail are natural partners.
The other side is that the human end user can use a variety of protocols to read and write e-mail. They can use SMTP if they are running their own MTA. They can keep the the e-mail on a server host, and use IMAP and POP to look at it. They can access it via text-based encodings (for example, when mutt or elm use ANSI rendering commands to put a message on their screen). And if the mail server happens to present the mail as web pages, then accessing those via HTTP transporting HTML is also a natural fit.
The important thing here is to always remember the distinction between MTA, MUA, and whatever mechanism the MUA uses to communicate with the human.
But bringing both together is the cause for about 100% of all scams, malware attacks, ransomware and other cyber criminal actions. It is in fact the absolute worst one can do.
Nonsense; e-mail based malware existed before HTTP and HTML were even a thing. Remember the Christmas Tree Exec, or Robert Morris' Internet Worm? E-mail is a good mechanism for transporting information, whether the information is good or bad. The flow of bad information is not caused by web-based protocols.
Furthermore, the original demand or usecase (people wanting to switch off their computers at night) is not even true anymore. Nowadays we are expected to own a smartphone that runs day and night, and to be reachable 24/7. There is no longer a technical problem in receiving your own mail at any time.
Smart phones do not even store mail (except for caching), they are just the visible surface of the MUA. Try the following experiment (done it a few times): Throw your smart phone into the swimming pool. Go to the store and get a new one (Apple or Android). Put the SIM card into the new phone after drying it, power up, and within minutes all your mail is back again.
But, the web based mail shops like Yahoo etc., being not only pernicious, but also superfluous now, nevertheless want to stay in place and continue to get fat on income from feeding their users with unwanted advertisements.
As explained above, we still need mail hosts (those machines that store mail), and MTAs. Very few people run their own. As we have discussed in this thread, it is possible to run your own, but it has become quite tedious. Whether it is worth it is a judgement call; IMHO, it is not worth it.
In the golden times of email, around 2000, when you met somebody at a conference and wanted to exchange further ideas in private, you would just exchange email addresses. It was easy to communicate, back then. Nowadays you don't get somebody's email address anymore, because it is considered dangerous to give it away (what good is email then, anymore?)
Nonsense. Several times this week, in interactions with various companies, the following happened: I call their 800 number, or bring up the chat bot on their web page. I ask my question, and they connect me to the correct person. I explain my problem to the person, they tell me their e-mail address and ask me to give a detailed description via e-mail, or send pictures of the broken part via e-mail. Then we have e-mail based discussions.
I'll ignore the rest of your paranoid anti-business rant. Angry much?
Providing own Internet Presence Services today, as a one man show, is like trying to maintain and fix own Tesla EV or any other modern vechicle - things will break enventaully which may lead to a bad crash 
