Is it possible to have vinyl nearly noise free?

Fleshler I always avoided playing an LP twice in a day as the prevailing thinking was as you describe. It is true the vinyl under the stylus is under immense pressure and is described as going liquid (never proven as far as I can tell). The mass of vinyl involved is so small that the surrounding vinyl acts as a heat sink and the temperature returns to normal immediately. I have a tire infrared temperature gauge and can not detect any change in the temperature of the record while playing. I think as long as the record and stylus are clean it is safe to play a record over again if you have too. But who wants to listen to a record twice in a day;-) 
"Last" is a joke. It is nothing but freon. You can prove this to yourself easily. With a dropper place a drop of Last on a glass slide and let it evaporate. Put another drop in the same place on the slide and let it evaporate. You can keep doing this a thousand times over and you will never see anything remaining on the slide. Nothing, Nada, Zero. That is how gullible we are. Will freon change the vinyl in any way? Absolutely not. It is totally inert which is one of the reasons it is a great refrigerant.
Lps are Lps. Some are quiet, some not. The best way to keep a quiet collection is do not buy used records. There are exceptions for instance if you are buying the estate of an expired audiophile who had so many records he may have played one once a decade. Make sure he did not buy used records. 

Atmasphere responded and explained that many phono stages use *active* negative feedback to reduce measurable distortion, but as the signal is recycled through the feedback loop, it lengthens the duration of the ticks and pops, making them louder and longer than they occur on the record surface.

I did used to think that was why- but it turns out it really has to do with stability in the design. So feedback isn't the culprit: poor overload margin and poor resistance to RFI are.

Our little UV-1 preamp employs feedback yet no ticks and pops.

In a nutshell, proper use of stopping resistors, good layout and blocking RFI at the input all contribute to a stable design. As I have often mentioned before, if the design is stable the need for loading resistors (if used with LOMC cartridges) won't be needed either. 

My experience jibes with what @atmasphere and others have been saying here. Once I moved up to a high quality phono stage (by Nick Doshi) my records have been generally silent. No need to buy expensive new releases to get that quiet - in fact, I prefer older, used records. The quality in new releases is too variable to justify the expense IMO. I do use a record cleaner, but mostly to get the best sound out of each LP and to protect my cartridges (learned that lesson the hard way). If a record is bad enough to sound crackly then I often find that a record cleaning machine doesn't help too much.  

so the simple answer to the OP is Yes, but you have to spend your cash wisely. 

so the simple answer to the OP is Yes, but you have to spend your cash wisely.

+1  That's it in a nutshell.

Yes, sort of.
Sweetvinyl.com
These units will eliminate 95% of the ticks and pops on the fly.  They do not currently eliminate surface noise, however, which will become more noticeable once the ticks and pops are gone.  The company says it will eventually offer a software upgrade to reduce surface noise, but it will not be free, owing to the complexity of developing the software.
I have the SC-2 as a beta tester.  You can find my thread on the Sugarcube SC-2 here on Audiogon.