In 2010, I purchased a dumb phone/sim card for use on a prepaid plan. At the time it was the only way to get onto a super cheap prepaid plan since they wouldn't sell you a sim/the plan directly. I then put the sim into my own purchased smart phones(multiple nexus devices and a one plus one). For convenience reasons, I refill my account online with a cc but I technically could simply buy the t-mobile refill cards for cash then activate the time on them.
As far as I know, there's nothing stopping me from doing this fresh again with a new prepaid phone and then never associating my real identity in any way.
I work in the telecom industry, and this behavior exists because it's not explicitly illegal. This type of data mining is just scratching the surface of their capability -- turns out that a combination of about 30 seconds worth of data scraped off http traffic (not https, though even https can tell you something) and a location are enough to identify most individuals and link them to a profile in a DMP -- which can tell you all sorts of information like which products you've purchased recently (both online and in brick and mortar stores with a credit card), any relevant demographic information, and even what kind of porn you like.
The real restraint on this has been in the use of this information. Marketers have been remarkably conservative in using this information; likely for fear of scaring off customers with "creepy" data. But rest assured they know more about you than you do yourself.
> your telco can know your home address based on a week's worth of location data
How accurate is that location data, do you know? Within 10 yards? 100 yards?
AFAIK you shouldn't have to get a throwaway phone either. "SIM Card Kit" or "Bring your own phone/device" may be keywords to research -- you should be able to get a SIM that you can put in any GSM phone, and it will come with instructions about a website to visit, or phone number to call, to activate it. If they insist on names etc and it's prepaid, you could give a fake name since it will have no bearing on your ability to use it, although I'd be worried that it might be illegal for some stupid reason.
I don't think this is possible in the USA anymore. I tried with ATT Verizon and Tmobile but I'm sure they are smaller players. All required somewhat my personal info altho for prepaid Tmobile did not ask for SSN. All told me this is due to the fact you're getting equipment "practically free". When offered to actually pay for it, I was always told "we don't have option like that".
Europe is much simpler. I walked into Play store [1], put $60 on table, and got USB dongle with prepaid scratch card of 6GB on a 3G network. No IDs, no documentation, nothing. Refills are very simple - you purchase a scratch offs for 3/6/9 GB or more, over the counter, no ID required.
[1] http://www.play.pl