Of course it's true. Essentially, you are confirming that having a top-5 pick is by far the most certain way to drafting "a number 1 on a championship team". Because if the team decides to acquire such a player via free agency, trade, or drafting in the 6-30 range, the chances are going to be way, way lower than 12%.
In the last 15 years there were only 5 players "who have shown this type of talent" drafted in the rest of the first round (Curry, Leonard, Giannis, Jokic, SGA), 5/(25X15)=about 1% chance per pick. And only one, Jokic, was drafted in the second round - 0.2% chance. On average, you will have to draft for a century in the 6-30 range (1 pick per draft) to draft a championship player, and for 500 years - by using only a single second-round pick per year.
Most of these players remained with their own teams, with only SGA, Leonard, and Davis changing teams via trades. I will be generous and add to this the Paul-to-Clippers trade, which happened within the same timeframe. So, there were 4 chances to obtain that caliber of players in 15 years. Almost all of the teams would be ready to trade for such a player every year, so we will conservatively estimate the trade chances as 4/(25X15)=1%. Finally, here are the chances for a free agent signing ( LeBron in 2010, 2014 and 2018, Durant in 2016 and 2019, Kawhi in 2019) - 6 cases. Almost every team would gladly create space for such signing, so the conservative chances are 6/(25X15)=1.5%. And these are extremely generous estimates, assuming that a small-market team like the Jazz and the Lakers have the same chances of getting LeBron or Durant via trade or free agency.
So, trying to obtain "such a player" by securing a top 5 pick has the 12 times higher probability of success than through picking 6-30, 60 times higher chances than drafting in the second round, 12 times higher chances than getting him in a trade, and 9 times higher than signing him as a free agent.
In short, no other strategy comes even close to simply getting the top 5 pick.
