The devil's in the details, but conceptually the thought is sound. The top 10 catchers in 2021 measured by WAR include 7 players who were age 30 and over. One more was 29. By that age, how they were originally signed/drafted fades into obscurity versus the decisions that cause them to be acquired or retained. The very top two, Perez and Contreras, were indeed international signings, whom their respective teams saw fit to pay even after arbitration.
Only Sean Murphy (3rd round 2016) and Will Smith (1st round 2016) were young guys in 2021 playing with the teams who drafted them.
Using that 2016 draft as a measure, it wasn't for lack of trying. White Sox and Angels also tried in that first round before the Dodgers took Smith, and then 6 other teams (including our Twins with Rortvedt) rolled the dice on a catcher before Murphy was picked. All those catchers could still contribute in some way going forward, but the idea of latching onto a top catcher with a high draft pick is elusive at best.
I mean, all draft picks are elusive, but it seems to me that the track record tells us that solving your catching problems through the draft is elusiver.