Contemporary Top 3 Picks for Each Team in the Finals:
Florida Panthers:
2010 - 3rd overall
2011 - 3rd overall
2013 - 2nd overall
2014 - 1st overall
4 Top Three picks in a five-year span
Edmonton Oilers:
2010 - 1st overall
2011 - 1st overall
2012 - 1st overall
2014 - 3rd overall
2015 - 1st overall
5 Top Three picks in a six-year span
I don't think that this is the right way to look at how to build a finals team. Many of these picks aren't even with their respective teams any more.
The Oilers key contributors are:
McDavid - 1OA 2015
Draisaitl - 3OA 2014
Bouchard - 8OA 2018
Hyman - Free Agent 2021
RNH - 1OA 2011
Ekholm - Trade Deadline 2023
Kane - Free Agent 2022
The Panthers key contributors are:
Tkachuk - Trade in 2022
Verhaeghe - Free agent in 2021
Barkov - 2OA in 2013
Reinhart - Trade in 2021
Forsling - Waivers in 2021
Bennett - Trade in 2021
Bobrovsky - Free agent 2019
The Oilers are built through the draft, but also have many key contributors that were signed/traded for.
The Panthers core was almost all signed, claimed, or traded for. The Panthers current roster demolishes the OP's initial claim IMO.
What does the makeup of these two rosters show? That a team needs a combination of strong drafting, good trades, and good signings to contend for a cup. Shocking news.