If you have a lot of meetings with external parties (it's not about scheduling between the 3 internal) a good calendar scheduling tool is worth it in my opinion. When I was a sales engineer at a software startup we probably spent 10-15 minutes per lead sorting calendar times out. Considering only 1 in 10 leads turn into sales this was 2.5-3 hours per converted lead.
By having a self service scheduling tool we already filter for the non serious people "I'm not wasting my time finding time in your calendar" and improve our lead quality while reducing the back and forth nonsense that no one enjoys.
Might be offtopic but adding friction might seem like a good time balancing matrix but what you are doing is filtering not the worst leads but probably the easiest ones to convert. Those willing to go back and forth on time will build muscle memory and make a deal easier. The others are still cold.. they will take additional effort during the sales calls.
By having a self service scheduling tool we already filter for the non serious people "I'm not wasting my time finding time in your calendar" and improve our lead quality while reducing the back and forth nonsense that no one enjoys.