I've had my eyes on the franchise since 2 but only got into it with 4...years after it's western release.
The first game I admit, just completly went past me, never heard of it when it came out. The second game did catch my attention but then I wanted to play the first game first, and it kinda annoyed me that the first game was english dubbed while the second was subbed, so I didn't bother in the end.
Then 3 came, and I was determined to finally get into the series...until, like you said, they decided to cut a bunch of quests and other side content from it's western localization. Even to this day, now that I'm into the series, I don't want to touch the game in it's current state.
Then Sega made it's biggest mistake...they released HD ports of 1 and 2 for the PS3 in Japan and I thought "Great, I can finally get into the series now once they come out in the west!", because the translations were already done and I thought releasing them over here was a no-brainer.
...but they never did. Huge missed opportunity.
When 4 came out over here I had faint interested but ultimately felt it was too late for me.
It's only thanks to Binary Domain that I still gave the series a chance, loved the game, learned that it was by the Yakuza development team which made me decide to fuck it and just get Yakuza 4 already. It was instant love, even if I never finished the game due to pacing issues with the character switching.