I understand why you would want such a feature but I don't think it would work. Neither as an additional way to improve sales or simply engage users who downloaded a free product.
1) I download a lot of free stuff just to play something random, other times it's to provide feedback, and sometimes I might actually be interested in playing the game for a long period of time. I don't particularly want to be spammed with emails from every single free game I happen to have in my library. You might try to argue "but I will only send quality emails" but the issue is it's open to abuse. Just because I downloaded your (free) game it does not mean I'm actually interested in updates, progress, or anything else really. If I paid for you game it's different - I only want email updates about a product where I spent actual money to buy it. At no point do you mention the ability for me to "opt-out". In fact, further on you suggest that if I don't provide my email then I shouldn't get to play your "free" game.
2) "What do you mean by email can be faked? That doesn't make sense" Yes it does. Email addresses can be faked for the most part. It's been a common thing for a long time. For example the place where I work uses SendGrid. Do you know what you can do with SendGrid? You can specify a custom "from" address for testing. I can send you an email from cia@us.gov or from yourbestfriendsemailaddress@gmail.com . It's only when you look further into the email sender that it shows as a "fake" email address and a lot of people are unaware of how to check it.
3) "if you don't have an email, then there is nothing to be collected then...my point is not to enforce anyone to provide anything, I really don't know your guys' point. Are you really getting the context of what I'm asking? Because it seems that you are throwing points that makes no sense for the sake of what I'm asking in this post."
Yes, people understand the context of what you are asking. At no point do you mention the ability to opt-out. So if I am signed into a free account and download your free game you are asking itch to force me to provide you with my email address by proxy of download. By downloading your free game you get my email address. This is a much lower barrier to entry than most people will accept.
4) "Then don't try it and don't provide it, is that simple. I mean, is not as if your email wasn't available already to itch.io, you already made that commitment, you got a user after all, for free, look how funny."
This is insidious and should not be how you reply to a potential player. "Don't want to give me your email? pfft. Fine! Don't play my game then!" It's one thing to suggest their email address can be collected, it's another thing to give an ultimatum - oh you're logged into an account and want to try my free game? give me your email address or you can't download it.
5) "For instance, if I make a free demo, to test if people are interested in the game and decide to keep developing the project, there is currently no way I can reach out these people that were interested in the game, there isn't a way to update them about the game, to tell them there is a new devlog showing some aspects of the game, in other words there is no way to build a relationship."
The key point you seem to miss is just because I downloaded you free game it doesn't mean I'm interested in future updates, your devlogs, or what you plan on eating tonight. The player has the agency to decide what to do. If I am interested in your game I will follow you, got Twitter? I'll probably follow you there too so I can get updates about your game. People who want to engage because they like your game will find a way to engage with you either via social media or something like discord.
Whilst I disagree with OP about this being a necessary feature it doesn't mean it's a totally bad idea. There are some use-cases where it could be useful. However, if this was added than there would have to be the option to opt-out. Yet, from what you said earlier it appears your attitude towards people who don't want to provide their email is "fine don't play my game then!".
Your position does not appear to be for the benefit of the player, but a way for you to increase your following in an inorganic way.
You're being a bit of a hypocrite. First you say you don't want to force people to give you their email.
"if you don't have an email, then there is nothing to be collected then...my point is not to enforce anyone to provide anything,"
but then you turn around and say that if you don't want to provide an email address... don't download the game.
"Then don't try it and don't provide it, is that simple. I mean, is not as if your email wasn't available already to itch.io, you already made that commitment, you got a user after all, for free"
Why are you insisting that people have to give their email address or "don't try it".
"I think that if I am providing something for free, in monetary sense, I should definitely get something in exchange."
No... you're entitled to nothing. How is it free if you demand something in return?
You're not being flexible at all. It might be different if you said "I would like to be able to email people who downloaded my game for free, but they should be given a choice to provide that email when downloading"
This game would like to collect your email address for blah blah blah
[ ] allow this developer to email you
[ x ] do not allow this developer to email you