Can you say what you mean by modern era and how you quantify influence and impact. And this is a genuine question as I'm curious to hear your thoughts explained more.
As someone that liked Bale and agrees with his points about the media, I just can't see how scoring some key goals in finals could make him more influential or have more impact on the team than Rooney did for us. Let alone Scholes or Giggs's impact for us and our success across the 90s, 00s and early 2010s.
Giggs was never the main character in a team - he was more of a support act for all his career albeit with moments where he took the game by storm ... compare that to Bale for Spurs, his performance vs Maicon being a key example.
What he did for Wales, Giggs would not be able to do - very difficult to carry a small team on your own back at any level of football let alone international. Giggs lacked the mentality to be able to pull this off and I don’t think he has the ability to be the star attacker and be the main goal threat etc. Bale is more powerful and has more of that main character energy.
As for Real, he was a support act but the moments he had in the biggest games - his numbers were also superior - scoring at almost 1 in 2 for 4 seasons before injury struck and the whole golfer phase kicked in. Giggs has scored only more than 10 goals twice in his entire career. His only advantage is longevity and superior agility but Bale is simply a better matchwinner.
Scholes similar - his England career doesn’t come anywhere near Bale for Wales. Can you imagine a prime Bale in some of the England sides Scholes got to play in and imagine Bale not having a greater impact considering their position (pound for pound).
Bale would have ended up being United’s star player whereas Scholes as much as he was an integral part of United as he matured, I again do not see Scholes dominating the side - it wasn’t really his character to be the star for a prolonged period. His moment against Barca in 2008 feels more of an exception than the norm... I can remember him being excellent against Real in those infamous galactico losses in 2003 but how many big game memories do we really have of Scholes compared to Xavi, Modric?
Rooney for me should on paper be ahead of Bale in terms of talent. If someone was to argue for him over Bale they would have a decent argument on their hands. He did have that main character energy but by playing second fiddle to Ronaldo and only ever starring at Euro 2004 (flopped every other tournament) in a far superior side whereas Bale Euro 2016 is as good if not better, followed by a solid Euro 2020 and we shall see if he gets them to a World Cup.
For real he was a support act to Ronaldo just like Rooney was but look at how he transcended that to score in big moments for Real where Ronaldo looked lost. Rooney had a greater propensity to getting pocketed. Having said that Rooney did lead a United team to 10/11 final, and in 09/10 was dominating Europe before injury at Bayern.
It’s more of a closer call. I can definitely imagine young Rooney having that impact on Spurs. I can also imagine him taking Wales to new heights. He could be talismanic.