@Larry L This would certainly be unexpected behavior as there are sites that process tens of thousands of requests every minute with hardly any issue. With that being said, there are a number of factors that can impact performance and as a result, we do not commit to certain performance levels. I should also add that the advice you received from the support engineer is likely more detailed than we can provide you here as they have the ability to access and review logs to understand where time is being spent on each request.
Some of the basic items that the support engineer likely had you verify is to make sure your web app and Azure SQL are both running in the exact same data center. All data centers are geographically a minimum of 500 miles apart and this can introduce enough latency to impact your site. Please note that one item in East US and another in East US 2 is not considered the same data center and risks introducing latency.
What exactly is your site trying to load? Pictures and videos? If so, you should consider moving those resources off your web app and store them on Azure CDN. Azure Web Apps makes use of network storage and while this is fast, sites with heavy pictures/videos can be optimized by offloading these files to Azure CDN.
Have you checked to see if your CPU or memory usage is high? Note that just because the documentation says standard tier or higher can run unlimited sites, there is a limitation at a certain point. Please ensure you aren't running lots of sites in a single app service plan.
Are you still working with the support engineer? What is the current status or final solution? If the issue was determined to be with your site code, they likely won't be able to assist much but I want to ensure they ruled out any platform issues impacting your site performance.