The way DSL based broadband works is that it's basically an add-on to a phone service.
£81 setup is fairly cheap. Virgin Cable often does free setups (if you take a phone line too...)
Agreed on all your points. I know the line rental is a major pain, esp if you have a mobile contract as well, and use the mobile for most calls. On the subject of Three I had a monthly contract with them from 2008 to 2012 costing 7.50 (later 8.00 /month) for 15 GB of data (which I fully used) but had stinging cost if it was ever exceeded. I started a mobile contract in Feb 2012 with them and was hitting 20-30 GB a month (yes, tethering can work even on non-One Plan accounts, but not recommended!) They could do no sensible deals to keep me as a customer this year so I switched but feel they generally offer good value for money.
As MarkJ pointed out, the customer can generally take any phone line service with some ISPs but Sky and TalkTalk bundle it together (and can be a pain to move away from afterwards).
To get a
phone line installed free (instead of 125 quid) then BT sometimes offers free install,
but you are tied in for 18 months and have to make a number of calls/month (or they charge more) and now that line rental is about 15 quid it's not a very cheap option. You cannot use their "line rental saver" option (more of which later) until after the 18 months.
Primus offers a new line for 59 quid and does line rental from about 8 quid (monthly payments) without the "line rental saver" that Plus.Net and BT offer ... which seems an underhand way to avoid the customer switching - in most cases
OFCOM has blocked telecom firms charging their standard monthly fee for the phone if you cancel - they are no longer paying Openreach for the line, so OFCOM says they can only charge reasonable rates of 2 to 4 quid a month.
BT and now Plus.Net charge their line rental fee monthly
or offer the lower effective rate
by paying for a year in advance,
BUT there is no refund if someone cancels 
It means they get around 10-11 quid a month even if you cancelled after 6 months.
Primus just charges a low fee (but at the very lowest bundle have no "inclusive" calls) so it's the cheapest that I've found. Of course it's a bit of a trade off - if you get Plus.Net on both broadband and line rental they don't charge the Fibre setup (they only charge 49.99 for a new phone line so still a bit lower than Primus). If you use Primus for the line not only do you pay the Primus setup fee but Plus.Net charges the fibre setup. However, the line rental being lower may mean a saving after
several years !
Even when Sky say they can install for free, their charges
can go as high as 105 quid - I was asking because I wanted a second line for fibre to be installed and checked many ISPs and options. Many offering cheap/free install will bundle their broadband too (and therefore are no good if user wants Unlimited Fibre account from Plus.Net).
Oh yes, I actually moved house to Merseyside to have the option of Virgin Media, but this is one of the streets where they have no service ! Mind you, I've been with PlusNet for over 10 years, so when fibre is eventually here (in a couple of months instead of last September) I will see if I can get some deal from them...
Finally, must remember why there's a cost for the line... while some may get noise and break at times, the overall cost is for the fleet of vans and engineers, plus the upkeep of the exchanges, and free repairs when lines are broken by trees etc. So we all pay a few quid for the copper to be maintained and service (for 999 calls etc) to still work if the exchange loses mains power (there are big batteries and backup generators to provide the 80V for the thousands of lines, to give dialtone whatever else is going on).