Does reverse proxy create a slower page speed and navigation?

I host 100s of high traffic, high speed, WordPress sites.

If a client asked me this question... I'd say...

This type of spaghetti setup is okay for a hobby site. Not for a real + money generating + pay your bills type of project.

For real (money generating) projects. Keep tech simple.

I run straight up Apache + FPM PHP + sites I host load test at roughly 1.1M request/minute throughput. You read that right.

There's all sorts of myths about what's required for fast sites.

My guess, 99.999% of everything written about fast sites is written by people who've never run a high traffic site or don't understand how to setup sites to isolation + fix slow points.

Do yourself a favor + hire someone smart to host your site.

In the long run, you'll save a truckload of money.

Reverse proxies can have a negative impact on page speed. It is difficult to completely answer your question without additional information such as:

Why is there a reverse proxy at all?
How significant is the performance degradation?

If you are interested, I can get on a call with you.

Depends on your specific setup and use-case. If you use AWS Load-Balancing you will get a managed service that will autoscale and will only have such a small latency that you can only measure it on a network point of view (milliseconds).
The advantage of using AWS Loadbalancing is that you will get detailed metrics that give you a detailed overview about latency, error rate on each of your services behind the reverse proxy. This way you can easily find the bottleneck.

Another possibility would be to setup a nginx reverse proxy running on EC2 instance. This way you could enable caching functions for specific locations and your reverse proxy will cache request. This way your reverse proxy can dramatically improve your perfomance but you might need to have rules for auto-scaling if you have a high traffic site...