There is a WU send limit of EUR 3000 within any 90 day period, this is now being applied to cash pick ups it seems also - so being realistic it is hard, if not impossible, to use it to shift large amounts.
I think the non-taxable limit for family support in Argentina is around ARS$140k per year per recipient. Amounts over this could be subject to taxation but trying to get concise info on this is difficult. I did ask someone at WU who apparently looked it up for me and gave me this bit info and I think there is something on the Argentine version of the WU website about this.
Taxation of remittances above this amount may in practice depend more on your tax status and liabilities in Argentina (e.g. savings may not be taxed as income but could expose savings that are subject to wealth tax, or funds that are sourced from income that should be taxed as income.) and I am not sure if sending to yourself really counts family support or not from a tax perspective, regardless of the WU classification. Probably there are some obscure BCRA rules on remitting savings to Argentina or similar that one should have followed and would be stuck with instead if it got opened up.
Have not found any accountants here who have a clear answer or guidance on using WU or similar products, but if one really wants to do it by the book and for larger amounts then it is possible to set up a CCL account with an Argentine bank and a foreign correspondent bank that is familiar with trading Argentine bonds. One can then remit savings or funds via this medium. Usually this is in the realm of private and offshore banking solutions, so US citizens will no doubt have issues with FACTA and banks not wanting the headache, but maybe there are US or US friendly banks that do it... All transactions must be declared however with a lot of source of funds info required, also it involves bond trading and delayed transactions, so it is not instant or without risk of getting less than you expected due to fluctuations during the "hold" period. A good number of Argentine individuals and companies with funds abroad en-blanco regularly use this option.