Is there only one real way to successfully build a team around recruits with certain attributes? In other words, if you don't focus specifically on a certain few attributes, is there a way to win by using another offense, defense, or some other strategy?
IMHO, no, there's isn't only one way. In D3 Rupp, US Merchant Marines consistently has top ten high ath/spd/d ratings. He wins a ton of games, and regularly wins 1-2 games in the NT. Conversly, my Marian team in Wooden D3 recruited at a C- to C+ my 5-6 seasons there. I had 40/40 spd ath and 50+ D and made S16 with 4 90 rebounders and 5 85+ per guards with probably around an average 60 speed. Yes, neither of these teams won the NT, but you can "build a team". The second question is requires so many variables I can't even answer it. I would say every team has to have good to great D.
Because I've also notice this has led to a great deal of recruits being highly coveted for specific skills while others with decent numbers overall are left by the wayside because they lack one or more of these specific ratings being very high.
Again, there are too many variables to answer this without me getting bashed on this forum. Yes, generally overall numbers are unimportant. Building your team with a philosophy in mind around your Off/Def is what is important.
I will name the attributes which seem to lead to success no matter the offense, defense, or strategy if anyone doubts what they are, but I assume most people already know. The rest of the attributes are like extra sugar on top of an already good food - nice, but if you don't have them in some or most of your players, you can still win or even build a dynasty.
So bottom line, is there one recruiting strategy to win as I suspect, or are there other serious ways to recruit and still win without those specific attributes being rated high in most or all of your players?
It depends on what you consider "success" and "winning". If you mean making S16 / E8 every year, then you can do so without elite ath/spd. For NT's, then yes, you will need elite ath in bigs, and competive ath / elite spd in guards. With D for everyone. And I mean consistent "whole team has great D", not "I have 4 guys with 90 D and 8 with 30 D". I guess what you are really asking is, can I recruit for other stats than ath/spd/d and beat teams that do? The answer is, you have to have least competitive ath, speed is more negotiable, but your D must be dominate. And your team should be elite in another category to compensate, preferably rebounding and perimeter.