I’ve come into working on multiple different headless sites developed by others who then walked away and left an entirely non-technical team to sort it out.
A well-built Shopify theme works great and plenty fast for even medium sized companies.
Since then Shopify has updated a bit (although not all that much, a lot of the issues remain) and we have had a wave of requests in the last year to build in Shopify - largely since none of the local marketing agencies want to touch headless.
It's been a bit disheartening really. I've been trying to get to the bottom of the marketing issues but I haven't been able to get clear answers on what they are.
Shopify also doesn't have amazing support for headless (double login on checkout is a big one), but with the rollout of their own Oxygen/Hydrogen platforms I've been waiting to see if they manage to solve these issues for their own solutions.
I’ve found though that often when clients say they need something that only a headless solution can provide, they actually don’t truly need it. And once the actual requirements are focused, a well built Shopify theme is plenty sufficient.
Maybe we are working at a different scale of companies though.
The main advantage of headless to me is the ability to get the speed of the site way up. But the nature of e-commerce is to add tons of pixels and other junk so it can defeat the advantages (and much harder to talk them out of adding pixels sadly…)
Our scale is a bit unusual, its more like high end small scale than large scale, think more like an architect designed house rather than a commercial building. As a result every site has some fairly unique features and Shopify often struggles with those. It's getting tricker to balance over time as the bar for a 'basic' store keeps being raised though.