Not at all - assuming you are UK based, you’d find it was the norm in countries like Germany and Denmark.
You can put babies in trailers from very young (be prepared for tutting and eye rolling here though). DS was in the Burley from 4 months. I got a ‘baby snuggler’ from Burley, specifically designed for tiny ones. Thule do similar.
I’ve only ever towed one child. However, l still occasionally take DS now 5.5 for a trailer ride - so weight would be similar with the larger trailer and combined weight of two kids. Make sure you get a decent trailer. They are much lighter, fold easily and most importantly handle extremely well (towed him down French/ Spanish mountain descents, and handled like a dream round hairpins at speed). If you plan to tow regularly it’s definitely worth the investment. We’ll never get rid of ours, as it’ll come in handy for transporting luggage when we cycle tour (once DS is a bit stronger/older and can cope with longer rides independently peddling). Like you say you could also use it as a buggy… but it’d be a bit tougher with a double trailer for that. I used the Burley as a buggy for a while… but preferred a sling as it was just easier where I live!
Trailers are just easier all round. Doesn’t matter if the weather turns, or it’s super sunny as the contents are properly enclosed. You can carry all manner of crap too in the cargo storage area - picnic, balance bike (🤣😂), toys, books. I’ve done thousands of miles with mine and never once thought “ooh, I’d be better with a seat.”
I’d really recommend looking at the Two Wheeling Tots and Cycle Sprog websites. They both take a no nonsense, sensible and practical approach to transporting kids by bike. Also to kids cycling.
DS rides his own bike now (he’s been peddling since 2.5). But even now at 5.5… I could not envisage him reliably peddling any distance. He’ll manage about 4 miles. DP and I live on our bikes, so it’s a normal everyday thing for him. So at 4 trailer! No point making life hard. I always find the towing time gives me some headspace and ‘me time’ which you won’t have if you’re herding a 4 year old. I do have a Followme Tandem (waaaay better than the trailgators and various other crappy gadgets) which attaches to my bike and his and I tow him from. He loves that. It’s super safe and stable. At 4, he’d have a tendency to start dropping off to sleep on it though 🙈🙄 But you still need to pop baby somewhere and all the ‘stuff’ you have to take for an outing with kids. So a trailer just seems easier. Mine handles well off road too - so gravelly paths. Forestry Commission fire roads kinda thing. Used it on some tame blue routes at trail centres too.
Cargo bikes feel pointless, although they seem to be all the rage for transporting at least three kids short distances in Germany. Again, I never thought I needed one (and I have a huge stable of bikes and love an ‘excuse’ for an extra).