It is a pretty fragmented market. In the US Western Union (public) should have the largest market share.
Each country usually has a dominant player or two that cater to their expat workers. India comes to mind with government owned postal service offering virtually free service to expat Indians sending money back home.
I suspect that there are two types of customers 1) people like me who occasionally need to send money to foreign countries and care about convenience more than price. I’d guess Remitly caters to this group along with Wise, Western Union and several others. I don’t think this is a huge market. 2) expats (think predominantly first gen 3rd world emigrants) sending money back home to their families. I suspect this is where all the money in this space is and it is fragmented and competitive.
My gut feel is that all these new companies like Wise and Remitly are taking share from Western Union for group 1 and are trying their best to get into group 2.
Just like in any business, it is possible to create superior product to anything else in the market. Stripe did that with POS. Remitly can do that in cross border transfers. My sole point here is that it may be a lot harder than their market stats make it look.
Another point I’d like to make here is about the nature of this business. At its very core, this is another financial company aka a shadow bank that needs to hold deposits in a bunch of countries with various currency controls and regimes. They are entirely dependent on the existing banking systems in the various countries they operate in. If one of the banks they hold money with goes insolvent… there goes their money. This happens far more often than you may think especially in countries outside of the developed world. They also transact with various FX brokers which too creates a bunch of risks including the so called Herstatt risk that could wipe them out completely.
Finally one more point, as any business dealing with money there is interest carry – interest company earns on cash sitting in their accounts. Transaction businesses like this always have some positive carry as they usually get money a day or two before they send it out and can earn interest in the meantime. I don’t know if Remitly discloses the amount of their carry I’m certain it is there and it may be quite significant. This of course this is subject to prevailing interest rates – zero or negative when rates are zero and more when they are not.
Check out this report re market in India. https://documents1.worldbank.org/curated/en/785341468269661757/pdf/662350PUB0EPI000India09780821389720.pdf