Why this matters
The executor is simply the person the will appoints to carry it out. Indian succession law does not impose a residence or nationality condition on that role, so an adult of sound mind living in the United States, the UK or the UAE can be named.
The friction is logistical. Banks and depositories run transmission processes with their own forms and identity checks; property involves local authorities and often a housing society; a court application may be needed. Someone has to be physically present for a lot of that.
What NRIs should consider
Pick someone who can turn up
An executor who visits India once every three years will struggle. A relative or trusted friend based in the city where your assets sit makes the process far shorter.
Always name an alternate
Executors decline, fall ill, move or die first. A named alternate avoids a court appointment.
An executor can also be a beneficiary
That is common and unproblematic. What they must not be is one of the two attesting witnesses, if they inherit.
Tell them in advance
Give your executor a copy of the will, the list of Indian assets, and the location of the signed original.
When professional legal advice may be appropriate
Consider speaking with a lawyer qualified in India if your estate spans several countries in a complicated way, if significant tax planning is involved, if a family dispute or contested estate is likely, if a business, trust or unusual ownership structure is part of the estate, or if you are unsure how a Will made where you live interacts with one covering Indian assets.