Possibly, those boys know a toe-tapper sure enough but two snippets of pop perfection for your consideration.
“the whole of the moon” by the Waterboys
and
“in between days” by The Cure
“Kiss Me” by Sixpence None The Richer
Love both of these.
Some post-punkish contributions
The Only Ones - Another Girl Another Planet
Buzzcocks - Ever Fallen In Love (With Someone You Shouldn’t’ve) (Actually there’s tons of Buzzcocks that fit here)
John Peel openly stated that the following song was the most perfect expression of youth culture of the 80’s - not one wasted second, get in, get out and don’t stay a moment too long , it does need to be played loud
Teenage Kicks - Undertones
For complete pop muzik its hard to beat Neil Sedaka - Breaking Up is Hard to do Randy and the Rainbows Denise You got the wrong Todd Rungren song, it should have been this one - I believe he wrote this as a reaction to being criticised for his music being too esoteric, and this was his way of showing that he could do easy disposable music and actively chose not to do so. Edison Lighthouse - Love Grow When My Rosemary Goes White Plains - Julie Do You Love Me Andy Kim - Rock Me Gently Lou Rawls - You Never Find Jackie Wilson - You Love Keeps Lifting me Higher and Higher Isley Brothers - This Old Heart of Mine I could come up with a hundred more but these are high up on my list
Don’t get me wrong - If you want to argue that Waterloo Sunset is the best song ever written, I won’t pick an argument - but is it flat out poppy enough to qualify? (Or am I reading more into the OP than I should - Pop Muzik Masterpieces?)
If it’s about the perfect Pop song…
Sugar Sugar by the Archies? https://www.youtube.com/watch?v=h9nE2spOw_o
Leader of the Pack by the Shangri Las? https://www.youtube.com/watch?v=Q8UKf65NOzM
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She’s So Young – Pursuit of Happiness
‘I’m so Dizzy’ Tommy Roe
To me, a great Pop song doesn’t need to be an important moment in music history. It doesn’t have to be a complex and masterful work of composition. It just has to make me smile, and have a catchy hook that sticks in my head for at least a little while afterward.
Many songs fit this criteria, but for now I’ll offer up two one-hit wonders and one of Pop’s all-time greats:
Walking On Sunshine - Katrina and the Waves
Do You Know What I Mean - Lee Michaels
Jackie Wilson Said - Van Morrison
Tough to beat 1976’s Boston hit More Than a Feeling as a perfectly-crafted pop song:
(In addition to others already mentioned, of course. I'm very fond of the OP-mentioned "They Don't Know," too.)I think they were channeling all of the fabulous Motown “boy bands” in the video, I’m not sure of their influences, they had a lot of hits, also as 10cc
Great suggestions here, I’ll be hitting up youtube for a while 
Another I like: Freda Payne Band of Gold
https://www.youtube.com/watch?v=Lnoyv4NGJzg
A few that still make me deliriously happy whenever I hear them:
Nick Lowe, Cruel to be Kind
The Vapors, Turning Japanese (also, Kirsten Dunst’s surprisingly competent version)
XTC, Generals and Majors
Ting Tings, Shut up and Let Me Go
Another one from around the same time as Nick Lowe, Jonah Lewie
https://www.youtube.com/watch?v=62eTq8ErUOQ
It’s not my favorite song (I’m a classical music guy, so I don’t really have a “favorite song”), but I think Billy Joel’s “Uptown Girl” is very elegantly constructed.
That’s the other one I came in to mention.
Regina Spektor - Ne Me Quitte Pas
Hey Julie – Fountains of Wayne
What, no Monkees songs yet? I’ll fix that: Pleasant Valley Sunday
Good one. Also Daydream Believer
Good one! Ok, they were a surrogate band, but most of their output was superb nonetheless.
And I thought of one more, because this thread also needs some Byrds:
The Byrds -I Feel A Whole Lot Better
When Tom Petty covered it on Full Moon Fever, he didn’t change much. He knew that it is a perfect song.
Just about any track off Beulah’s The Coast is Never Clear is pop music refined to a razor’s edge; standouts are “Popular Mechanics for Lovers” and “What Will You Do When Your Suntan Fades,” but for “perfect pop” I’ll go with “Hey Brother.”
Letters to Cleo - Co-Pilot
Another brilliant pop band is Rilo Kiley. They have a ton of really great stuff but here I will submit “It’s a Hit” (ironically, it wasn’t a hit, but that’s not really the point).
I love the Byrds, but I know their stuff so well, I can listen to them in my head. But “Feel A Whole Lot Better” is worth actually dragging to my exclusive “Tunage” playlist*… Along with Roger McGuinn’s “If We Never Meet Again” (and Jules Shear’s original). Another perfect song…
*A lot of what’s been mentioned is Their Only Song on My Phone…