If you imagine a doll's house what do you see? Quite likely it is a very lovely, if traditional, home fitted with charming, tiny custom-made items.
There is a neat parallel between this and a custom-built website. They too are unique (at least in some ways) and they may be beautiful (though opinions may differ). But they are definitely fragile & very expensive!
Unfortunately, the parallels end there. Children rarely need to upgrade their doll's house - they grow up instead. Professional Services marketers have no such luck - this fiddly, bespoke object needs to be constantly upgraded to fit with the ever-changing needs of the digital marketing landscape.
The original in-house sponsor has left. The original agency has quitted the scene. Everything takes ages to do and costs a fortune. Maybe worst of all, when you do upgrade you have to recreate all of the little add-ons and tweaks in the new version so the process repeats itself.
Don't have a doll's house. Have a Lego Castle instead.
Quick to construct, deconstruct or upgrade - often with less specialist knowledge (an 8-year-old, for example). They are flexible, modular, and future-proof. Need a drawbridge? There you go. Ramparts and trebuchets? No problem!
That fundamentally is the benefit of a composable, headless approach to your website build. Use best-in-class building blocks to build your tech stack and swap them out when required. Your agency can focus less on the internal workings of a particular technology and worry instead about how you are meeting your strategic goals. Anything else is a bit mad.