I +1'ed Andrew's answer, but I'll add something else which I think cuts closer to the heart of the issue.
Standard has the lowest power level of all the constructed formats. It has the fewest "safety valves" - here meaning options for decks to counterbuild against an overpowering strategy. In Legacy for example, if a Red deck becomes overpowering, opponents can always add Blue Elemental Blast to their sideboard. If Black is too powerful, they have Veil of Summer. Failing everything, there is Wasteland and Force of Will. In Standard, these safety valves are much weaker. To quote an example from recent Standard (I am not familiar with the current metagame), The Immortal Sun is a safety valve against all planeswalker strategies, but it's 6 mana with no enters-the-battlefield effect. A superfriends deck can conceivably remove the Sun and keep pumping. If the superfriends deck is overpowered, then the Sun would still help, but it would not be a decisive sideboard card.
This means Standard is the most fragile of all constructed formats. If you print a powerful card, it's more likely to unbalance Standard than any other constructed format (with some exceptions).
When you have a set that cannot be used in Standard, you can print cards that would likely unbalance Standard without unbalancing other formats. An example of such a card is Seasoned Pyromancer. This card was printed in Modern Horizons, which is legal in Commander and Modern but not Standard. Would this card have unbalanced Standard? I suspect it would. It's a fair card, but its effects are very powerful, and it's resilient against hate. Another is Minsc and Boo, Timeless Heroes. It's a 4-mana 4/4 with haste and trample and is a planeswalker with 4 starting loyalty that snowballs in one turn if not removed.
This does not mean that there is a Commander card in recent sets that would have been overpowered in Standard, but it does mean that R&D could've designed the Commander cards more freely, because they don't have to worry about knock-on effects on Standard. Another way to think about this is that Modern, Commander, etc. have a higher power level than Standard. If you can only print cards that are Standard-legal, then you are less able to impact the Modern metagame (and therefore keep Modern players excited) without breaking Standard apart.