The law in Argentina is similar to that in your own country - like most others - as to having specific requirements that determine whether a company a tax resident or not and the mere presence and roles of its final beneficiaries have a lot to do with it. Where a companies clients are located from an Argentine perspective is entirely irrelevant. You can't just wish the law away with wishful thinking when it is not convenient to what you want to hear. If you are actually serious about doing serious business from Argentina with a US company, I strongly recommend you speak to an Argentine lawyer or tax accountant and not an internet forum.
If however you were "just" a freelancer / consultant sending an invoice to a company each month (up to predetermined limits) you can easily register in Argentina as a monotributista. No idea however how this helps for immigration purposes, but whatever solution you choose, don't go overcomplicating things that are not worth overcomplicating.
While I would be afraid of Argentine corporate taxes due to the complexity and many layers of them that are more trouble than they are worth unless you are talking big business, I would not be afraid of Argentine personal income taxes - 35% as a maximum rate is really not that bad compared to most developed countries albeit it does have low thresholds and lacks scope to make sizeable deductions. What sucks in personal taxation is the global wealth tax that will drain you dry once/ if you stop making money.