Lucky you. In hindsight I wish I had gone for it, just to have another option.
Let's hope something new will come up.
The US side is clear: The US LLC is disregarded for tax purposes. From a tax perspective it does not exist.
Simply put: If phi303 as a person does not owe taxes in the US (why would you if you never even worked physically from the US), then the US has no tax obligation.
Yes, if you have employees in the US, there will be tax, but I believe that would even be the case if you as phi303 hired an employee in the US (sole proprietorship), so it's the same thing.
On the side of the other country, it really depends how they view the US LLC. Some countries will view it as transparent like the US (all income of the US LLC is taxable as your own income), some countries will view it as a corporation, and in some countries it will depend on the details of the articles/shareholder agreement of the company.
If you operate under your own name, there are no "headquarters". The income would be seen as self-employment income. Most high-tax countries would tax all your self-employment income from all over the world anyway - unless a treaty limits that right (usually because some other country also wants to tax that income).
But with a company, the "headquarter" thing would indeed happen:
If you live in a high-tax country with an aggressive tax authority, like France, Germany, Denmark etc., and you register e.g. a BVI shell company (not a transparent entity, but no substance in the BVI), then the tax authority will also claim that since there is no true office anywhere else, the "headquarters" must be where your tax residency is, even if you claim that you only do work for the BVI company while traveling abroad.
It would be a different story if you incorporated a company in another EU country, you rented a proper office and you could show that you travel there frequently. Then it might be believable that you actually only work from that place and not from your home country (but even then, things like CFC rules could spoil this, especially if they think you only chose the setup to save taxes).
To give a concrete example:
Say you are an expert for Soviet-era mainframe computers and you live in the Netherlands. There are no Soviet-era mainframe computers in the Netherlands, so it's not possible that you would be doing this work in the Netherlands. Once or twice per month, you fly to former Soviet republics and you help them fix their problems for a fee of $10k per day.
If you bill them under your own name, this income would be taxable in the Netherlands as self-employment income, since the Netherlands taxes the global income of its tax residents.
But even if you use a BVI company to tax them, this company will be tax resident in the Netherlands as they will say your headquarters are in the Netherlands, you probably enter into agreements from there (you reply to emails confirming projects etc.), you make strategic decisions there. Where else would your "office" be if not in your own home?
With a US LLC, it will be the same thing, depending on whether they view it as transparent (then it will be self-employment income), or if they view it as opaque - then they will treat it like the BVI company.
But let's give another example:
You set up a company in Georgia, rent an office Tbilisi and hire a local director, a salesperson and another technician. They handle all client inquiries for you since they speak Russian, you are not actively involved in the business.
Every now and then you fly there for meetings, sometimes you also fly to visit clients for the very difficult cases.
Could this company still be taxable in the Netherlands? Maybe. It would depend if they can show that you still do some kind of work from the Netherlands, maybe you still decide what they should do while you're in the Netherlands? But at least this case probably would be a bit harder, I would asssume.
Or finally:
You live in Italy, but close to the border with Switzerland. You set up a Swiss company and you rent an office and you drive across the border every day to work from your Swiss office because you have Swiss clients and you want to be closer to them.
Would Italy be able to tax this company? Probably not.
But from what I have heard, Portugal view US LLCs as opaque (so they would not automatically tax all money that flows through the US LLC), and they also don't enforce PE rules. They basically don't care. I'm not sure if you would need any kind of office anywhere.
Disclaimer: I'm not a lawyer, so please don't just take my word for this. You'll want to double check it - I may have misunderstood something. But the basic concepts would hopefully be mostly correct.
