I think some definitely do, though the temptation is probably strong most places. LDS Missionaries are somewhat unique in how strict the standards are. They are called to serve for 18–24 months somewhere in the world (they have no choice) and during that time don’t consume any non-religious media, date, travel outside of their assigned area, or work. They have only a few hours on one day per week that is a “Personal Day” to grocery shop, do laundry, write home, or do approved tourist activities. They also adhere to a strict dress code (which is why you always see the young men in suits with name badges).
Missionaries and their families save money while growing up to afford these missions. The price of a mission is the same for everyone, but is then disbursed according to the cost of living in the area. If you served in Guatemala you would require a lot less than if you serve in New York, but you pay the same. If the family or individual can’t afford it, then the church typically provides using tithes or other donations.
Missionaries’ time is spent giving lessons to people learning about the church called “discussions,” fellowshipping active and inactive members of the congregation, volunteering at local organizations (food banks, park rehabilitation, etc.), and studying scriptures. The idea is that you are able to exclusively focus on your spiritual life during your mission.
I personally didn’t serve a mission, but my younger brother did and one of my sisters plans to. Many missionaries say it was a wonderful period of study, prayer, and self discovery- but it can also feel somewhat isolating and disconnected.