Having just gone through this process (opening a bank account), as well as purchasing an apartment last year, I can give you my experience. My wife is an Argentinian citizen, and we live in NYC. Last year, we bought an apartment in both of our names. It was a rather difficult process to do remotely, and it only worked because we have family in BA. This year, I worked on getting my DNI and opening a bank account, also a difficult process. Here are some of my observations that may help you.
1. To move any substantial sums of money into Argentina, you need: (a) a CUIT from AFIP, which you can get without a DNI, but you do need the Domicilio; (b) proof of provenance of the funds (I used US tax returns and a statement from my accountant, both of which had to be translated, but they didnt require an Apostille - others have reported needing an Apostille); and ( c) a local bank account which allows international wire transfers (I used Banco Piano, which charged a rather high transfer fee, and used a NY bank as an intermediary - but I think things are easier now). While the local bank account will require a DNI, I was able to get around that by having my sister in law open the account, and then I provided her a power of attorney.
2. I tried, unsuccessfully, to get my CUIT in person during a 3 week visit in 2015 - by the time I got my Domicilio, I ran out of time to get the CUIT. You need a local address for the Domicillio; apply in person to the police station closest to the address; they will process it in about a week, and deliver it to the local address - you don't have to be there in person to receive it, but somebody has to be present with your passport in order to get the Domicilio.
3. I later found out that its much easier to use an attorney to get the CUIT from AFIP -and they can do this remotely if you have the Domicilio.
4. You absolutely need a DNI to open a local account. I checked with numerous banks, this seemed to be a firm requirement.
5. I was told that I needed to show pay stubs showing funds in order to open the account. They would take a foreign pay stub, but this bank (Santander) wanted it Apostilled and translated - in the end, we were able to use my wife's pay receipts as she is an employee of the Argentinian government.
6. Since my wife is Argentinian, my process to get a DNI wasn't too hard - it took about 2-3 months for me to get all of the docs, translated, Apostilled, etc. here in the US, then certified at the Argentine Consul in NYC. They pasted a visa in my passport indicating I was a permanent resident. I then had to enter Argentina with that visa, make an appoint at Migraciones for the DNI - I brought all of my paperwork to the appointment, they took a photo, fingerprints, and gave me a receipt with a tracking number (not the DNI). It took about 9 days, but I received the DNI at my local address (the one you use for your Domicilio). Note - you have to be physically present to receive your DNI, and have to have your receipt from Migraciones as well.
7. I admire people that are living permanently in Argentina without a DNI - I have found that, even for me as a sporadic visitor, doing many things in association with my apartment was very difficult without a DNI - it is used as a universal ID in Argentina, and I can't imagine living for any length of time without it. That said, I know many people do this.
Hope this helps a little.
S