You will be amazed by even a formal request process can become chaos. At my current job, even with a request process and a ticketing system, requests are either being lost all the time or we need to deal with them immediately so they won't get lost.

I don't think is that simple. It needs proper design and someone on top to watch and pull the strings from time to time. At least in the beginning until this becomes the norm and people can pass it to new people without getting lost.

Alternatively the person getting the request could put it in a queue.

That's still a "request process".

the thinking here is that if a PM is managing 3-4 projects with 5-8 people per project at any given time, there are potentially hundreds of questions/requests that come in per day. Yes - some come in through tickets but rare is the time that is so regimented. just putting them on a list requires an assistant until now until now