I don't think the reasoning here is sound due to incomplete consideration of all possible scenarios and conflating separate and irrelevant concepts as supporting arguments for the conclusion.

First, what are we even talking about, precisely?
"alts vs BTC, not vs USD"
What "vs" means here is maximizing BTC as opposed to maximizing USD.
Just being clear about the topic so we don't talk past each other or have these words mean different things to different people.

Short answer 1:
If BTC drops against USD (i.e. USD rises vs BTC), then all your alt gains relative to BTC is not worth a lot of USD, which is what you care about for purchasing stuff - at least until the real purchasing power of BTC becomes better than USD purchasing power, widespreadedness, and acceptance (effectively "replacing" the dollar or at least gaining the same status as USD in terms of acceptance as a currency to do commerce with).

Short answer 2:
If every alt coin was available to trade against USD, not just BTC, would you still be saying the same thing?

Long version:
If you have 3 entities, USD BTC ALT (e.g. ETH), then you can have the following possible rankings for percentage change.

1. USD > BTC > ALT
2. USD > ALT > BTC
3. BTC > USD > ALT
4. BTC > ALT > USD
5. ALT> USD > BTC
6. ALT > BTC > USD

You described scenario #4 and #5 in your 3rd and 4th paragraphs respectively.
You cherry-picked 2 out of 6 possible scenarios and said it was all the scenarios, but didn't take into consideration the other 4 scenarios, which may (and does as will be described) undermine your conclusion.

The conclusion you made is this:
"Any way you look at it you will always make bigger profits if you trade against BTC only."

A word of clarification here:
"against BTC" means trading something priced in BTC, NOT choosing to hold BTC.

In the 4th paragraph aka scenario #5, where ALT > USD > BTC, the profits in terms of BTC may be higher. But if the real purchasing power of BTC is lower than the real purchasing power of USD, then your "greater profits" in terms of BTC is only in terms of BTC, which if it goes down, is not providing you with more purchasing power (i.e. real profit).

Another point:
You do mention the case where BTC going down against the USD as an overall trend.
But in principle, you should care about it at every point at every level, not just the overall trend.
The price decision is based on things in the moment, just like every trade is.
Why be sloppy and approximate about the BTC/USD levels? That affects your actual value.
Would you be sloppy about a 10% difference in a trade, or does slippage and fees actually matter? Of course they do. So would the fluctuations in BTC/USD in real time.

"I will put everything into USDT & wait for the correction to finish so that then I can buy more BTC for cheaper than I sold."

What you said there has nothing to do with trading ALTS against BTC vs trading ALT in such a way that is priced in terms of USD.
That is trading and timing decisions, just like when you say "Then why would you have your money into ETH vs USD if you know you'll have more profits having your money into BTC vs USD?"
First, you don't know what will rise or fall. That is the nature of trading, reality, and predicting the collective decisions of all of the relevant agents affecting the price of things.
Second, to say "you should have invested in the thing that went higher" has nothing to do with what your goal should be.
This as a supporting argument for maximizing BTC as opposed to USD is a complete non-sequitur.

The true ultimate goal is to maximize purchasing power.
It's messy, but for now, it is largely USD.
Prices of most goods are far more stable in terms of USD.
Most things can't even be bought for BTC presently.

So as long as maximizing USD more closely adheres to maximizing real purchasing power, no matter what you trade, whether it be stocks, commodities, BTC, Alts, etc., you should be concerned about maximizing it in terms of dollars.

Eager to hear your thoughts.
And props for raising the topic.