It's not a bad thing, I think they phrased it poorly. If you're doing network operations or devops work at an ecommerce business, then in a gaming company, then telco, yeah you'll definitely be more well rounded.

If you're a developer at these companies, and you try to claim you're an expert in each of these fields... yeah I'm going to raise an eyebrow.

I don’t think it’s terrible either. But if I’m reading your resume for a non architect position, I might be thinking that your going to come in, learn the field for a year, and then leave. That’s not the most attractive hire.

I guess the company's response is also interesting for me. It could be yours. Or it could be: this is a person who can fill in another role in the future and will already have a lot of company experience. (I get that this is not possible under some reasonable company size)

Alone, it's not. However, when you are "Changing jobs very frequently and [have] no consistent theme in jobs", then you don't really have much experience that would help you toward an architects role.