Customer Required Attention - Quantitative Measurement

Hi all, 
My first post in the community ;-)

In my company, today we're assigning CSMs to new signed accounts based on a mix of parameters such as  ARR, Region, Vertical, Industry, Product-Expertise.
But we are realizing that none of these parameters would actually reflect the amount of time/attention that particular customer needs/requires.

So my question is:
Are you giving a "Customer Attention Score" to each customer, in order to assess how much time consuming it is?
It might definitely be handy when assigning CSMs to customer.

And if the answer is yes:
- How is it done ?
- Which parameters are you taking into account ?
- How frequently this score is reviewed ?
- Do you have clear boundaries with customers that are demanding too much?

As stated by a CSM in my team: "The # of customers doesn't matter. I'll just spread my attention and the level of proactiveness differently depending on it".
Should it be the case ? Or should we create a list of actions that should be done by a CSM in order to reach the 100% for each customer?

A bit long, so thank you if you got to here ;-) Your feedback will be highly appreciated !