It depends on who you are and what you bring to the table. It's a very different story if you've got a few thousand EUR/USD worth of untaxed money that you want to hide vs. a six–seven figure amount of clean or clean enough money. Why do you want an account? Why should the bank open one for you? As a non-resident foreigner, you pose a significant risk to them. Risk costs money.
Armenia: there are some banks you can try but the trend in the country is towards not allowing non-resident foreigners as easily anymore. SMS is still popular for 2FA with many banks and they only send to local phone numbers.
Belarus: sanctions making banking a big pain if you transact to/from western nations. Bank accounts can be opened by non-residents but almost never remotely.
Cambodia: can be opened in person relatively easily, but almost never remotely.
Dominican Republic: possible to open as non-resident, but banks rarely do it for non-residents.
Guatemala: same as Dominican Republic, but more difficult.
Mongolia: IIRC, there are a few banks there where you can open personal saving accounts in MNT for long-term deposits. Otherwise, not much going on there.
North Macedonia: Silk Road Bank
and Halkbank sometimes open accounts for non-residents. Not sure about remote.
Papua New Guinea: no.
Paraguay: very rare for non-residents.
In many cases, forming a local company with 1-2 local directors will be enough to increase your chances of opening a corporate and a personal account. Some of the countries above are quite attractive for business due to tax or cost of labor.
Honestly, just get your affairs in order and stop chasing non-CRS
banks. Most of these countries are going to be engaged in CRS in the next few years anyway. There is no long-term stability in secrecy.
If you don't want to pay tax, move to a place that doesn't have any tax.