I run a free API www.macvendors.com that handles around 225 million requests per month. It's super simple and has no authentiction or anything, but I'm also able to run it on a $20/m VPS. Looks like API gateway would be $750+data. Bummer because the ecosystem around it looks great. You certainly pay for it though!
In circumstances like these, I've estimated per-request costs of systems at tens of dollars.
It's likely more spikey than that (i.e., peak/off-peak times), but certain server-to-server loads have a very consistent load pattern. (For example, at Userify - SSH key management -- servers check for updates every 90 seconds or so or 10 seconds for premium plans or self hosted, so the load pattern is literally a flat line.. extremely predictable. We'll probably switch over clients that can handle it to websockets and maybe hashed etags and cut that load pattern into oblivion, but for now it works and is simple/auditable code/extremely reliable, which is a very important factor in our case.)
To GP's point, spiraling costs are definitely a factor with most of Amazon's services such as DynamoDB and especially Lambda... they are sometimes an effective use of devtime, especially in the beginning of a project (and when dealing with a mature platform like DynamoDB and maybe not so much Lambda), but you have to carefully consider the cost factor as you scale. For example, Lambda is often literally several orders of magnitude more expensive than an equivalent ELB. (i.e., it can be more than 100x more expensive.. for small scale or maintenance tasks, that may not matter.. for a heavy/core service, it definitely matters!) So, as they taught us in AWS SA, design for cost: use the more advanced services when it makes sense, but optimize across all axes, not just devtime.
TL;DR: most cheap cloud instances can do 85req/s.
I'd be happy to have 85req/s hopefully by then I'd be charging lot of money.
Having said that it's a struggle to figure out how to get Laravel running on ELB