I'm all for welcoming opposing opinions but when you've only played 2 out of 7 games and say "don't listen to him" regarding which order to paly them in it's kind of hard to take you seriously.
That's fine but there is a key reason I would play 0 before 1 and 2-7 couldn't possibly change that.
IMO 0 sets up the relationship between you and Nishiki and makes 1 so much better because of it. Trying to imagine playing 1 without knowing the real bond you have with Nishki just doesn't make 1 nearly as good as it was playing it after 0. Sega just did a magnificent job at setting up 1 with 0. I couldn't stop rushing through the story in 1 because I wanted to know what happened to my boy Nishki. It wouldn't have meant as much to me without 0.
Now if you have reasons for why the original way is better I'm willing to listen to them. Also almost everyone recommend playing 0 first. From gaming websites to reddit. It's the most common choice. They even did a poll and 0 won with 60% of the votes. Also when you say it's the intended order did you read something straight from dev or are just assuming that's the case because of the order they were released?
I haven't played Kiwami myself (but have seen it played by a friend), but two big reasons make 0 a bad place to start if you're looking to play through the whole series IMO. The first one is the gameplay will spoil you, and you will expect a lot of features and functions that simply aren't there. This is somewhat mitigated if you play Kiwami and Kiwami 2, but it'll feel even worse when you get to Yakuza 3 at that point.
The second, and much more major one, is something I won't go into too deeply because I don't want to spoil anyone, is Majima's character. Since you've reportedly only played 0 and Kiwami and started with 0, you probably don't understand how much you're missing of Majima and his development by seeing him in 0's light first. It's a massive disservice to anyone experiencing the series IMO.
As for the points you brought up, all of this is experienced just fine by playing 1 as it is. I had the exact same feeling you did without playing 0 first, because the story engrosses you immediately and establishes the bond very strongly. That doesn't disappear if you haven't played 0. 0 didn't exist when I played it and I felt all that urgency just fine.
0 also has a ton of references and easter eggs to later games which anyone who starts with it won't understand at all.
It's definitely possible to start with 0, and SEGA took care to make sure that it is a viable starting point for anyone who wants to get into the series, but I'd say that anyone who does so is doing themselves big harm storywise, and making it more difficult mechanically to enjoy 3 and 4 after it.