grammar - In front of "ほうがいい," is it always past tense?

ほうがいい means:

the particular way "ほう" is "が" good "いい"

So, for example, if it looks like it's going to rain, I might say to a friend:

"今日は雨らしい。傘を持った方がいい。"

But what I'm curious is, why is "持った" past tense? It feels like it means, it WOULD'VE BEEN good to carry an umbrella, so it feels quite inappropriate tense-wise. I ask this question because there's no distinction between future and present tense in Japanese. For example,

"明日来る人は私の友達です。" The dude coming tomorrow, is my friend.

"今、あそこから来る人は私の友達です。 That dude coming our way, is my friend.

So logically, I thought "take your umbrella" would be: "今日は雨らしい。傘を持つ方がいい。"

Instead of "今日は雨らしい。傘を持った方がいい。"

So, why is it that it's past tense?

Answer

This 〜た is the perfect, not past; that is, it's indicating a time before some reference time, rather than a time before speech time:

傘を持っていったほうがいい。
Lit. "Having brought an umbrella would be better."

That said, I don't think native speakers actually have such a complicated model (of comparing possible future worlds, one of which where you have brought an umbrella), but rather 〜たほうがいい has just become a way of making suggestions; that is, I think the 〜た has become mostly semantically bleached. However, I'm pretty sure this was the original function of 〜た here.

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It is also possible to have the plain form of verbs before 〜ほうがいい, but they don't have a future interpretation but rather a "general" or "habitual" one.

傘を持っていくほうがいい。
"Bringing an umbrella is best."

That is, you're not making a suggestion about something to do at a future time, but making a more categorical statement.

I wish I had an explanation of why it's impossible for the plain form to have a future interpretation here, but I don't.