Another thought: did you notice? the top 5 are direct variations of the .30/06...
What I also find interesting is that the five top-ranked cartridges (and the tenth) all share the same design trade-off: usable power vs. usable trajectory vs. usable shootability, based on the proven performance of the .30/06 in two World Wars.
1- The .270 Win is a necked down .30/06. You could call it the .27/06.
2 - The .308 Win is a modern rendition of the .30/06. You could call it the .30/52 (1952).
3 - The .30/06 is the American baseline reference of "do anything anywhere in anyone's hands".
4 - The 7mm-08 is a necked down .308. You could almost call it the .28/06 (in the shorter .308 brass).
5 - The .243 Win is a necked down .308. You could almost call it the .24/06 (in the shorter .308 brass).
10 - The .280 AI is an Ackley improved .280 Rem, itself a necked down .30/06. You could call it the .28/06.
A very strong case could be made for the .30/06 to be the American entry into the "universal" cartridge competition. But it was/is not perfect. For many applications it was/is over powered, and to many it was/is recoiling too much.
Everything flowed from there.
-- The .270 Win trades "excess" .30/06 power on PG for flatter trajectory and lower recoil.
-- The .308 Win (7.62x51) trades "excess" .30/06 (7.62x63) power on PG - and enemy combatant - for lower recoil and lower bulk (shorter brass).
-- The 7 mm-08 capitalizes on the .308 shorter brass and trades "excess" power on PG for flatter trajectory and lower recoil.
-- The .243 Win goes all in on the .308 shorter brass and trade of "excess" power on PG for laser-flat trajectory and virtually no recoil.
And everything else non-magnum since then has either tinkered on the edges (e.g. the .280 Rem is a .28/06, the .35 Whelen is a .35/06, the aptly named .25/06 is a hidden gem deserving a lot more popularity) or has duplicated a .30/06-based round, with shorter fatter brass, sometimes pushed to the ridiculously impracticable: try to chamber from the magazine a round of Winchester Super Short Magnum (WSSM), or even Remington Short Action Ultra Magnum (SAUM)...
As to the two magnum entries:
7- 7 mm Rem Mag
8- .300 Win Mag
they both trace back to the .300 H&H Mag which triggered the same type of necking up and down on the basic hull, from .244 to .458.
In the end, and this does NOT surprise me -- and I will take it as validation of my general skepticism about "new" cartridges -- only the currently ubiquitous 6.5 Creedmoor and the 6.5 PRC make the top 10 list, and I would strongly argue that they are mostly modern marketing gimmicks chasing the 6.5x55...
An American poll
No doubt this is an American poll, and Europeans would likely see things differently. Or the same, but from a slightly different starting point.
I suspect that a European poll would likely show a similar genealogy with the 7.92 Mauser (8x57 a.k.a. 8 mm Mauser) and derived cartridges 7x64, 9.3x62, 6.5x57, 6.5x55, although - interestingly - the 7x57 has all but vanished from Europe (for example, Blaser does not make a R8 barrel for it...) after the 7x64 replaced it as the "universal" European, or at least Continental, caliber.
When I bought my .270 Win in the 1980's in France, you only saw them in the Alps, with an equal distribution of .243 Win with those who did not have opportunities to hunt Red Stag or plains' Sanglier (wild boar), and the rest was 7x64, with also an equal distribution of 9.3x62 for aptly named running boar hunts. I would speculate that the bolt action market in France then was 40% 7x64, 30% 9.3x62, 10% .270 Win, 10% .243 Win, 10% everything else.