I've been working with Lambda for about two years now, I'd like to answer all of your concerns. I don't work for AWS but I do love Lambda and I think it has its place amongst everything else. Previously I built node.js+Postgres apps hosted on DigitalOcean for ~4 years.

>What if you want to send telemetry to a third party?

Can't you do this from your own Lambda code? Sure, your code could crash before it can reach your telemetry service - but isn't this a concern on a server based app as well?

>Or use a cache?

Elasticache or Mongo or whatever NoSQL 3rd party service you want to use works straight from Lambda. If you're talking about caching Lambda responses, you can again add custom code, which you would also have to do in a server environment.

>Or deploy something bigger than 250MB?

Yeah, you're SOL here. 250MB is huge for any non-GUI software and it would take a long time to get set up on Lambda's containers. If you're in this spot, I wholeheartedly recommend ditching Lambda for EC2. However, don't count Lambda out entirely - you can still have it take over repetitive, simple tasks so the server hosting your monster 250MB backend doesn't get overwhelmed!

>Or handle WebSockets (without having to read/write state in DDB on every message)?

I'm sure when PHP introduced sessions there were a bunch of devs complaining about having to maintain a MySQL table for session keys. Ultimately, if you're making a web app, 95% of its routes are probably glorified Excel formulas, so you'd need to pull and push state through a database anyways.

Where else do you store WebSocket state? In memory? What happens when you got millions of connections at once (think slither.io scale)? At the end of the day you have to put it into something that can scale. I'm assuming if you're using Lambda you care about scaling up - otherwise you could literally run your backend on an IoT toaster with a MySQL database hosted on some IoT coffee maker that had "admin" as its root password and nobody would tell the difference. Again, if this is you - Lambda wasn't meant for your use case. Go buy a coffee maker.

>Or buffer something on the filesystem?

I'm not really sure how to answer this one. There is obviously no permanent file system on Lambda unless you count S3 (although I'm sure you know that).

I did some searching and found this: https://stackoverflow.com/a/31660175 If you're talking about uploading huge files, direct upload to S3 seems like your best bet.

>Or run something for more than 15 mins?

Lambda wasn't meant for this. Set up a server and schedule a cron job. I'm guessing if it takes >15min it's probably some kind of backup, statistical analysis, ML model training, database dump parsing, yadda yadda yadda...Lambda is for handling events. Everything I mentioned seems like an internal business operation the users have no part in, so that also seems like a good candidate for just having one server instance floating around and throwing all your odd long jobs onto it.

I haven't used Lambda Step Functions, but I vaguely recall hearing something about being able to run long tasks with those? Not sure. I wouldn't bother, though, I'd just head straight for a server (the example Amazon gives is starting a job to retrieve a specific item in a warehouse, sending an order to an inbox, and waiting for a warehouse worker to mark the item as retrieved...I don't know why Amazon chose that specific example, but it sounds like they have a very specific target audience!)

>How do all those things not impact agility?

I'm of the opinion that tools do not impact agility, decisions do. If you decide to use Lambda in a situation where a server would prevail, you're wasting time on the wrong thing. If you decide to a use a server in a situation where Lambda would prevail, you're...not really doing anything wrong, I think. It'll likely cost you more than a Lambda function but those numbers only start to matter once you actually have to care about scale.

Like I said, it's ultimately about what you're trying to do. Don't put a square hole through a rectangular screw, or something like that.