My Linux experience is old and very limited. I have used AWS for years for other things (S3, cloudfront, transcribe, etc.).
Initially I setup an elastic beanstalk app/separate mysql instance on my own AWS account just so I could quickly deploy (all new to me).
Then I setup the app on my client's VM, had to configure Apache, .net core app, service, mysql, mailing.
I would say the elastic beanstalk stuff took about 3 hours (some problems with IAM and Amazon's visual studio plugin, basically ended up having to use my master key). Setting up the VM server, plus a new way to deploying .net core apps and learning/relearning much of linux took 4-5?
So no significant savings there.
Deploys are a few clicks from VS on EB, and take a little longer to the VM, but only because I haven't bothered writing a script that I estimate would take me 1/2 hour at most, in reality probably 5 minutes.
I have clients on (windows) servers that have been running for 10 years with little intervention from me (had to clear some space a couple of times as that client's app saves large files just in case, but they are all backed up on S3 as well).
TL;DR; in my experience DevOps part of running a startup/small enterprise app is basically trivial, a rounding error, compared to time spent on development.
Edit: The move from CapEx to OpEx is not about savings, it's often about shifting the costs in your books.
Some businesses would require huge up-front investments without the likes of AWS. DevOps costs might overwhelm you pretty quickly once stuff like compliance becomes a factor, for example.
Sometimes it's not about the technical issues, but documentation, process and qualifications. In B2B there's plenty of that and just the bus factor [1] alone might force a start-up into considering a cloud provider.
In the end it's not just shifting cost, it's also shifting risk and standards and that may or may not be a critical factor.
or in other words, shifted nothing?
There is others reasons for example the flexibility, the managed services, etc. but I don't think this one makes sense.