Mutiple binary classification for for best propensity to buy one of the product

Problem:- I have 5 products for sell and I can pitch only one product in a month to one customer.so I wants to know which product customer can buy.

Proposed solution:- I build 5 binary logistic models to understand the probability of each customer to buy particular product. where I am getting 5 probabilities. so what ever model is giving maximum probability amongst 5 I am pitching that product to customer

for an example If we have Product A,B,C,D,E to sell and so does 5 propensity model

Upon running this propensity model for Customer1

we are getting following results

IN THIS CASE WE WILL SELECT PRODUCT D AS IT IS HAVING MAXIMUM PROBABILITY

But in order to generate training data for couple of month I run randomized campaigns where i randomly sent pitch for particular customer and observed among those how many customers purchased same product from us.

Now that we are running this model now we get slightly improved results but sells lift is still not as expected.

There could be several different problems with model but I have slight doubt on approach I wanted to understand is my approach correct.

Question

as we are building 5 different propensity model with different population and different event rate . so whether there probabilities are comparable.(Because we are taking max probability product and pitching them for same.)

if those probabilities are comparable then buying seeing table above can we say that that customer having exact same chances of buying Product A and Product E