I agree with you :)

Even on the same network, I like having a Zigbee coordinator with an Ethernet port. I put it in a more central location in my house, which helped improve the network quality.

As others have mentioned, VPSes (and rented dedicated servers) count as self-hosted. In many situations, a VPS can make more sense than a home server:

• Better internet connection - a lot of hosts have 40Gbps connections now, and it’s a data center grade connection with a lower contention ratio.
• Cheaper upfront - no initial purchase cost.
• Depending on electricity prices, it can be cheaper over the long run too, especially with a $20-40/year one (see LowEndTalk, GreenCloudVPS Budget KVM, RackNerd specials, etc). That’s the case for me in California - just the electricity for my home server costs more than some of my VPSes.
• Usually better hardware than you’d have at home - often AMD EPYC or modern Xeons (not a 10 year old E3 or E5), enterprise NVMe SSDs, etc.

AWS is very expensive compared to regular VPS services, and you only really get a benefit from it if you use a lot of different AWS services in a multiple regions. One EC2 instance in one region doesn’t really have advantages over a regular VPS.

If you do want to use AWS, consider using Lightsail. It’s like a regular VPS and has a fixed monthly price for some amount of disk space, CPU, and monthly transfer, father than being dynamically priced.

my Home Assistant server with z-wave, which needs to be physically nearby my other stuff

Not sure about Z-wave, but with Zigbee it’s possible to get coordinators with Ethernet ports (and this is generally recommended over USB ones due to the added flexibility), so your Home Assistant server doesn’t actually have to be near your Zigbee network, just the coordinator does.