Well they shouldn't take up 'the mantles' of these characters. Each became the heroes they are due to unique circumstances. Not a costume to put on and be the superhero. Iron Man was a tech genius with money and had the armor built as his heart had shrapnel in it. The suit helped him live. Superman is from a destroyed Krypton. Batman is a playboy with cash and was a detective who sought out seedy criminals. Spiderman was Peter Parker who was bit by a radioactive spider in a freak accident and gave him the powers. Captain America was injected with the Super Serum in the 1940's. Each also became popular due to the fact they were fully fleshed out, unique characters who many could relate (or envy) and made us love them. It would be (and is) stupid to replace those people with new faces to carry the 'mantle'. It doesn't and shouldn't work that way. Created new characters, not bury the popular original ones.
Well, you better time-travel back to the 1950's and tell them not to create Hal Jordan or Barry Allen who ironically went on to become much more popular than either Alan Scott or Jay Garrick so your last point is kinda amusing.
Also, why shouldn't it work that way? Simply saying it's "stupid" or "shouldn't work that way" isn't a very good reason to me, heck the latter is kinda frustrating because that just limits story potential if this were NEVER allowed to happen. A new character is a new character regardless of what their superhero identity is. Hal Jordan was not Alan Scott. And most of the legacy characters do have their own personalities, goals, supporting casts, etc., thus they are by definition unique characters. The powers should not be what defines their characters so there shouldn't be an issue with legacy characters. Your descriptions of these characters are pretty shallow as they only focus on powers and their talents, you don't mention Tony's cockiness or struggles with alcohol, Superman's desire to always do the right thing, Peter's constant poor handling of his social life, etc. If the legacy characters had these exact personalities then yeah that's an issue but most of the time that's not the case. Like, good god, I'd begin laughing if someone claimed Guy Gardner was anything like Alan or Hal.