There are actually more pros then cons for the "home countries" in my opinion, and I have official/credible sources to back this opinion up.
Financial remittances have been recognized as an important developmental vehicle associated with migration. Financial remittance flows have steadily increased in volume from the 1990s to the present day. In 2017, migrants sent an estimated $466 billion to families in developing countries. Money sent home from abroad is shown to be more stable than both private debt and portfolio equity flows, and several times larger than international development aid.
An estimated 800 million people worldwide are directly supported by remittances from relatives and loved ones abroad, according to the International Fund for Agricultural Development (IFAD). Remittances lift families out of poverty, improve health and nutrition conditions, increase education opportunities for children, improve housing and sanitation, promote entrepreneurship and reduce inequality.
However, apart from financial remittances, transnational communities also contribute by way of 'social remittances' - the flow of skills, knowledge, ideas and values that migrants transmit home. The impact of social remittances was most strongly felt in areas such as education, health, employment, business and aspects of governance, found a study conducted by IOM in Tanzania in 2014.
In short, there is a lot work to be done. IOM, UN Migration Agency, in partnership with specialized organizations, civil society, academia and the private sector, have engaged in several concrete projects and initiatives aimed at improving knowledge of social and financial remittance usage and corridors. They have conducted studies on the impact of remittances on families and communities, and worked to enhance the development impact of remittances, financial inclusion and diaspora engagement.
EDIT to address cons:
There are indeed cons; let's look at the ones you pointed out: inflation: I think most people would say this form of inflation is insignificant when you compare it the global economic perspective. There is a literal currency war between most if not all of the worlds nations, going on for a while now, where advanced economies are technically importing inflation to emerging market economies. These amounts are huge and when you factor in our topic here, it makes our topic a bit insignificant in comparison. See: https://en.wikipedia.org/wiki/Currency_war
James Rickards also has a great book on the subject.
As for social conflicts, this is a pretty micro oriented con, and a bit political as well. I'm afraid I don't have much knowledge on this one.
For accelerated emigration, this is perhaps the biggest con, but is easily countered in the long run. Here's why:
I think it is commonly accepted that most of the skilled workers in the long run wish to return to their home country/their families. When these workers leave their home countries, the country loses the potential GDP input of said workers. What do they gain in return? Cash inflow. Which we already accepted doesn't have much of a significant effect on inflation. What that cash inflow does do is increase consumption and investment a little bit, which promotes the prosperity potential of the country in the long run. Assuming this consumption and investment is aimed at long term growth for the home country, the workers would eventually come back(their original goal in the first place) to a stable economic system(that they inadvertently helped create) and provide further.