"I could not get an entry ticket to 'Shotput' because it was sold out" a common complaint, isn't it? No! There are many sports like that which is not a crowd puller. 'Crowd pulling' or 'business' is not a criteria for Olympics. But in fact 'history' is one of the most important criteria for sports in Olympics as stated here: https://theconversation.com/how-sports-get-chosen-for-the-olympics-62917, and Wrestling has it all!
Now, imagine you want to watch an important match of a particular game. But Olympics cannot give you a set time. As many matches like Boxing, Wrestling happens match after match. This uncertainty can also take the crowd away and many may never see the highlights either. In my case I just check for a video on twitter feed that defines key moment. Team sports like hockey and football has fixed schedule. So it is almost impossible to verify which sports is the most popular. Income from a sports can of course be measured but then wrestling won't be the last on that criteria.
The reasons for exclusion seems to be made up and is one sided, which if applied to other sports in Olympics, might lead to the exclusion of many sports. There is still not enough evidence to what lead to such a decision to take down a popular sports. Unlike some said here, it is very popular in many European countries such as Hungary. And most Eastern European countries have Russia influence and culture and Wrestling is a culturally important sport for Russia.
The only conclusion which I could come up with and supported by people here(link below), is that the committee who ever was tasked to do this had people from countries that were not good in wrestling. Or could be those who are jealous of countries who are a powerhouse in wrestling. Or in other words silly human jealousy and hatred could be the reason for such a decision. Olympic committees have had such 'human' fights all the time and will continue to do so. Because not everyone has an MBA degree and if they had they wouldn't be there!
Another issue that could have lead to the exclusion could be the internal fights and biased referring and other mal-practices with in the Wrestling community. eg: Wrestlers can bite and leave marks on the body of the opponent and no punishment will be meted out(even if there are rules preventing it). So if one sports in Olympics take more resources for problem solving('technical criteria') then there is something wrong with that sports and must be eliminated. It could also be that some ex-wrestlers/administrators in the committee could have back-stabbed their own federation. If this was the case then this exclusion gave an opportunity for introspection and then wrestling came back as a new and better sport. Which is something we all prefer in the end too.