Cold start vs scaling to zero trade-off in FaaS

Question

Before I even start, I'll say that I was not 100% sure whether SO is the appropriate SX for this question. Let me know if I should ask this on some other SX.

The question is about FaaS in general, but if you can better explain this in a context of a particular FaaS platform/provider, that's great as well.

I'm currently reading up on serverless computing (FaaS to be more specific) and trying to get myself somewhat comfortable with the subject. Now almost everywhere I turn, I encounter the following statements about FaaS:
1) Most FaaS platforms support down-to-zero scaling;
2) FaaS providers charge their users based on their function execution time (usually measured in ms);
3) Potential cold starts (i.e., creating a new instance instead of reusing an existing one) are an issue in FaaS as they considerably degrade performance of your application;

Points 1 and 2 are considered benefits - you get exactly what you need (including nothing at all, if applicable) andy pay for exactly what you get.
Point 3 is considered a drawback - the request takes considerably more time to complete. I've seen authors describing cold starts as a sign of FaaS platforms not yet being mature. I've seen practitioners saying that they set up periodic requests just to keep their functions from becoming inactive and "going under" thus triggering the cold start the next time it's called.

My question is - why are cold starts viewed as undesirable instead of as a trade-off?
What I mean is, considering that the user pays for execution time in FaaS, wouldn't it usually be in their best interests to avoid having warm, but idle function instances? To me it seems like a cost vs high availibility decision. Do I misunderstand something? Does having a warm, but idle function instance does not count towards one's execution time? Even if so:
a) isn't it undesirable from the providers' perspective (having to allocate resources that are neither used nor paid for)?
b) sending periodic requests (as mentioned above) surely does cost you, right?

Answer 1

For this answer, I will talk about Azure Functions. The answer will more or less transfer to other serverless providers.

The cold start problem results in the delay of the execution of a request made by a particular client, the time for servicing of the request during a cold start results in approximately from a 5 second to 50 second delay. This is bad because of these reasons:
1. Many functions are time limited, i.e their execution is halted if the execution time exceeds a particular limit. So some users do not get their requests serviced.
2. The time to serve a particular user is quite variable and this is always undesirable while designing an application since consistency is key.

Whether Azure Functions is a cheaper alternative or using a dedicated App Service plan is cheaper depends on the Application and the Number of Users you are trying to service.

Azure function charges the users for Resources consumed (Resource consumption is calculated by multiplying average memory size in gigabytes by the time in milliseconds it takes to execute the function) as well as for Number of Hits. So yes, the pinging function created to keep the functions warm does cost more, but cost is not the main point to switch to a FaaS model. A FaaS model is primarily used for creating Fault Tolerant Services, so if one part of your API messes up the entire application does not need to go down.