I am pretty sure atc is grateful and appreciative when pilots 'help' them with their arduous task of moving and spacing aircraft. You know, pilot has ads-b or tcas and can see the 'exact same thing' as on the controller's scope. So he notices a 'better way' of working the flow, eg: "Approach, why don't you let me turn in now, and go ahead of that slower twin on the 15mi final, it might be a lot more efficient". Thoughtful and helpful, right?
Depends. They have a plan for you from the outset and may be limited by LoA or other rules you can't see. And no, pilots do NOT always have the same view on their traffic system the controller sees. So your "helpful idea" may just be radio blather they don't need. Or it might actually be helpful.
I definitely wouldn't add wording like "it might be more efficient" to an idea transmission like that. I'd just say, "we could accept a heading of XXX to intercept early if that helps" -- they already have the picture and know what will work and what won't, and have been doing their job a lot longer than I have!
I'd be interested to see what controllers think of "helpful" pilots and how often it's really helpful and how often it's just extra noise.
Stuff where it has "worked" or the controller seemed to like it was things like you mentioned, a quick "we can do it slightly non-standard to help you out" and stuff where it seemed not to be a big deal was stuff like ...
"Cessna XXX radar contact lost, we'll pick you up again in about 30 minutes. Remain this frequency."
"Okay thanks. We could accept higher if you like."
"No need. Radar is spotty there at your altitude but it's not a problem."
"Roger, Cessna XXX".
The other time being "helpful" seems to work is if they forget a Bravo clearance or something and it's too busy to get a word in edgewise so you legally and properly descend...
"Cessna XXX I see you now at 8500 descending, cleared into the Bravo airspace, maintain 8500." I knew they just forgot the request, no big deal.
And the constant bane of the non-GPS driver given a direct clearance...
"Unable to accept direct, we are slant alpha equipped but we can accept a vector until receiving YYY and heading 320 looks good."
Never had a controller not take me up on that offer, yet. Haha. If it's quieter I'll change that to "but we are vector qualified!" for a chuckle.
The one I've never ever had a TRACON controller take me up on is the offer to descend below a Bravo and continue on course when we've had to deviate a significant distance off course. You can offer to get out of their hair and below the controlled airspace all day long and they'll never take you up on it around here, anyway.
If you were really way off course and being vectored all over hell and gone, you could honestly force the issue and just say you're doing it, but I usually don't. "We will descend to XXXX and then cancel flight following" isn't really necessary, but I sometimes want to when they've needed to give me a tour of some lovely place, 20 miles off course.
"Negative, just stay with me and I'll have direct for you in X miles."
LOL. Controllers want to control. I can't blame em. It's what they do.