I have to call out your take because it's either outright wrong or is overgeneralizing, to put it politely.
A lambda is just someone else's computer running your function, which you call through a fancy rpc interface. There is no infrastructure.
Just because you can and should deploy a lambda with infrastructure-as-code tools such as CloudFormation or CDK, it still does not make a lambda "infrastructure". It's just your function running on space CPU cycles of someone else's computer, which you call through RPC.
Running your lambda as a background task in someone else's computer does not make it infrastructure, just like running code in your own server is not adding infrastructure.
Also, it seems you're missing the whole point of offloading background processes out of your servers. If they are computationally demanding and your servers are well provisioned them a background task can lead your system to scale up. You don't change the way your system is deployed or is operating if you run your background task as a lambda. You make a request and things run just the same. Zero potential for alarms and being paged in the middle of the night.
And more importantly, for some usecases lambdas are entirely free. Does this have no value to you?
Some people feel compelled to criticize everyone around them just to feel self important. A little humility would serve them well. Just because you fail to understand something's traits and properties that does not mean everyone else around you is wrong and you are the only enlightened soul who is right.