Back in my early (teenage) era of gaming, henchmen were important. When I spend my summers in the Poconos, at best we had a group of 4 - most times it was 3, and 1 of those 3 was obviously the DM.
Initially we played with DM PCs (yes, I know how bad that is) and we quickly learned that didn't work well, especially when the DM placed treasures with his PCs in mind. Therefore, we moved to using henchmen to flesh out the party.
As this was AD&D 1e, and we were mere teenagers interpreting Gary's rules for recruiting and using henchmen as best we could (or as best we could in our favor.) Our henchmen never broke ranks and ran. Never betrayed a party member. They were fodder for the PCs quest to earn gold, magic items and expo.
My group in NYC rarely lacked players and when it did, only one member of the party sought out a henchman, who later in turn became less henchman and more NPC party member (but not DM PC.)
I can only recall one instance of party members seeking out henchmen in my return to gaming these past few years (torchbearers and hirelings have been used and abused.) We ran a funnel of sorts to see which potential henchmen would survive to be hired, but that campaign wrapped up shortly thereafter and they didn't get used.
So, from my perspective, it's "nay!" for henchmen and "eh!" for hirelings.
Where do you stand?