I agree but it depends on the strategy:No, it doesn't matter.
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3) You have a EUR account, fund with EUR. Just before you trade you sell EUR and buy USD. You buy a USD instrument. You aren't paying interest to borrow USD (nor do you earn EUR interest, but that is irrelevant). This is good, and apart from the conversion is equivalent to (1).
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GAT
For instance, in case of day trading, nothing is required. At the end of the day one gets his or her USD P&L.
In case of investing, buying USD seems correct but one ends up with FX risk. If one wants to cover this risk, then buying USD for 125000 EUR implies buying one EUR.USD futures contract. So, investing in USD the equivalent of 30000 EUR is not enough to cover the FX risk with one EUR.USD futures contract and the USD risk remains.