US Broadband is slow because that's the state of the infrastructure -- the infrastructure is very expensive to build out, and most of the country can't support a broadband build out.
It may surprise some, but the majority of the United States is not serviced by a cable television or internet system:
What happens if you scale that map so that regions are sized according to the population within the region rather than the geographical area of the region?
Or, to put it another way, is the majority of the US population serviced by a broadband Internet service provider? the FCC's "Eighth Broadband Progress Report", from August 2012, says that the percentage of the US population "without access to fixed broadband meeting the speed benchmark", said benchmark being 4Mb/s down and 1Mb/s up, is 6% (5.9% of households), with the figure for rural areas being 23.7% and for non-rural areas being 1.8%. So the majority of the US population is serviced by a broadband ISP (by the FCC's 4Mb/s down/1Mb/s up definition of "broadband") - and even the majority of the rural US population is.
Why is an area not serviced?
By "serviced" you presumably mean "serviced by broadband Internet access above some speed threshold"; what is your threshold? Presumably it's better than 4Mb/s down/1Mb/s up, as most area that actually has people in it is serviced by services that's at least 4Mb/s down and 1Mb/s up.
So how about municipal broadband? Take the private company out of the picture and make internet a government service and it must get really cheap, right? Well, Bristol, Virginia is considered the most successful implementation of Municipal Broadband right now. This village of 17,000 people offers fiber optic connections to its residents for....roughly the same price as TWC or Comcast (for comparable speeds) and far far more expensive for 1GBps service ($320/mo) than Google offers.
And Google's service is a little under twice as expensive as the 1 GB/s service Bredbands Bolaget offers - 899 SEK/mo (the rate after the first year) is USD 137.73/mo at the current exchange rate. That, in turn, appears to suck relative to, say, HelloVision's $31.47 (at the exchange rate at the time for the South Korean Won) for 1Gb/s up and down, according to table 2 in the New America Foundation's "The Cost Of Connectivity 2013", but I don't know whether that's a first-year teaser rate or not (Bredbands Bolaget's first-year rate is, at the current exchange rate, $73.31).
The facts are this:
1. Huge portions of the country cannot be cost effectively serviced by high speed internet access.
How high is "high speed"?
3. Most large population centers do not have enough potential 1Gbps residential customers to make it cost effective to upgrade the equipment in those locations to support 1Gbps connection speeds -- businesses can already get those speeds and more but it is not inexpensive.
[Citation needed] What statistics do you have for the number of potential 1Gb/s residential customers in those large population centers?
4. New entrants with deep pockets don't have to deal with replacing equipment that is still being used to pay for the debt taken out to install it in the first place, but they will.
They do, however, have to deal with installing equipment in the first place.
5. More options for internet service in a community mean lower market shares for the participants, which means lower revenue from the market, which means lower return on the installed assets required to offer service, which means either raising rates or exiting the market.
...or living with lower profit margins.