I wouldn't say that I prefer games where you can customize your character. Games with character customization and games without both have their place, and I like them both. However, character customization can sometimes come at the cost of other qualities I find important.
For example, one of my favorite franchises is Fire Emblem. Since Fire Emblem: Heroes of Light and Shadow (a Japanese exclusive game, a remake of Fire Emblem 3 which is the second part of Marth's saga) and Fire Emblem Awakening, which were released back in 2010 and 2012 respectively, most of the games released since then have had avatar characters which you can usually customize to an extent. Fire Emblem Echoes: Shadows of Valentia was an exception since it was a remake of Fire Emblem Gaiden, the second installment in the series and which had pre-existing characters in the lead roles. Also Byleth and Shez from Fire Emblem: Three Houses and Fire Emblem: Three Hopes are set in their designs, aside from Byleth being able to change to different costumes, but they are still avatar characters. Prior to this, the games had designated characters called Lords who were the main characters of their games, like Marth, Ike, Eliwood/Hector/Lyn, Roy, etc. Avatar characters seem fine conceptually, but in practice a lot of the time these characters in modern games are just lauded with praise from other characters since it's the player's character and I guess you need to be told how awesome you are for playing this video game or whatever. I lay all this groundwork to get to my point that, in this instance for example, the solid storytelling and tone of the older games have somewhat gone to the wayside in favor of giving players a character that they can self-insert if they want so they can romance other characters. I recognize that this is a popular aspect and helped draw new people in over the past decade to keep the franchise alive, and I don't begrudge people for their tastes, but I feel like the series has lost some of the identity it used to have and a good portion of what got me interested in the first place. I'd say this can sometimes be a source of tension between some older fans and some newer fans, though there are also plenty of people from both camps that can also just enjoy both styles when they try them.
So, with that in mind, I think it's important for developers to really consider what it means to implement character customization in a preexisting franchise that didn't have it from the start and what impacts it might have.
I'd say, as someone who puts importance on games with stories actually having good stories, if I had to say I prefer one or the other, I prefer games that have predefined characters that the writers give personality, drive, ambition, meaning, etc. That's not to say that it's an all-or-nothing thing, there are probably games with character customization that still have good implementation, but yeah.
Now, if we're talking a game or series that always had character customization, or that implemented it and does it well, then hell yeah, customization is awesome. I love customizing characters and can sometimes take hours in a character creator. I like changing my characters' clothes, hairstyles, etc.
Character customization is fun. It is not, however, necessary for me and in some instances I'd rather it not be an option.
Tangentially related, I wish there were more games where you find equippable items that actually change your appearance. For example, in Shin Megami Tensei IV, you can change up your clothes, hairstyle, etc. and it actually changes Flynn's appearance, but in other RPGs, equippable items are just something that affects stats but doesn't cause any visual change. I know that would require more budget, time, etc., but it's just something nice to see when it's present.
