Yes, but gTLDs (basically anything other than two-letter ones) are subject to higher reliability standards. You’ll have some with a worse reputation than others (like your .men example), probably depending on their pricing/popularity, but they should all generally be reliable.
Two-letter country code TLDs are held to no standards by ICANN, and could literally be entirely hosted on a single server in the basement of some island country’s government building if that country wanted. I wouldn’t purchase a domain on a ccTLD, even one masquerading as a generic TLD like .me, .io, or .co.