This is a US-centric answer, which may not apply in other countries.
Given that credit card companies have access to your credit information, why do they keep advertising balance-transfer options to people who have great credit and never carry a balance?
TL;DR answer: The credit-card companies hope that you will accept
the offer so they can make a quick buck off you that they otherwise
have no chance of extracting from you.
The phrase "never carry a balance" means that the card-holder is paying
each month's statement balance in full by the due date and is thus not
charged any interest on purchases. Generally, people with excellent
credit scores receive balance transfer offers (and often checks that
can be used to pay taxes or auto loan payments etc or deposited into personal accounts) which are indeed charged 0% interest for 12 months
or 18 months etc, but which have a "service charge" of 2% to 5%. Those
"0% interest for 12 months and no service charge" offers that you
see in advertisements are sent to people with middling credit scores.
For what happens when someone used to paying off each month's
statement balance in full accepts a balance transfer offer, see this previous answer of mine.
All credit-card companies that I have used set the minimum payment due
on each monthly statement to be the sum of (i) all interest accrued
over the previous month on earlier purchases, (ii) all interest on
cash advances from previous months as well as the current month, (iii) all service charges (including annual fees, cash advance fees etc), and (iv) 1% of the sum total of all purchases and cash advances that have not
been paid as yet. The statement balance includes everything that
is currently owed including the 0% rate amount. But what if you
(someone
used to paying off each monthly statement in full) have just accepted
a 0% balance transfer offer of (say) $10K with 2% service charge?
You have no past unpaid purchases or cash advances, but do have
current purchases of (say) $4K. The full statement balance is $10K + $200 + $4K = $14,200
while the minimum amount due is $200 + 1% of ($10K + $4K) = $340.
So you decide to pay $4200 by the due date in the belief that you
have paid off all your current purchases and the service charge,
and so you are all clear for next month. Buzzt! Not so at all.
Any time that you pay less than the full statement balance, the
CARD Act says that the minimum amount due part can be applied to
any part of the statement balance; it is only the excess, if
any, over and above the minimum payment amount that must be applied
to that part of the balance that carries the highest interest rate
(and then to the part of the balance with the next highest interest
rate and so on till all the excess amount is used up). So, of your
$4200 payment, $340 will pay off part of the 0% loan balance of $10K,
and the rest will be applied to the service charge (paid off completely)
and then to the $4K purchase balance. Worse yet, your account changes
status from "Last month's statement balance paid in full" to
"Last month's statement balance not paid in full" and so all future
purchases on the card will be charged interest from Day 1, and so
will those purchases that you didn't pay off be charged interest.
That is,
there is no 25-day grace period anymore. If you want to continue using
your credit card, the only way to do it is to pay the whole $14,200
statement balance by the due date of your next statement. In short,
you will have paid $200 as "interest" on a loan of $10K for a period
of 26 through 55 days depending on when in the billing cycle
the balance transfer occurred. (Note that the $200 you are paying
is technically a service charge, and is not subject to usury
laws that forbid exorbitant interest rates).
For those people with less than stellar credit who don't look
at the credit card statement closely each month and simply pay the
amount shown as the minimum amount due each month, a 0% balance
transfer offer with no service charge is, for the credit card
company, the gift that keeps on giving (which is why they can
offer no service charge). Their customer is
paying off the 0% amount due, and none of the payment is being
applied to the interest accrued last month, and so the
interest-bearing part of the balance is increasing! Furthermore,
12 or 18 or 24 months later, the customer is quite likely not
to have the wherewithal to pay off the remaining 0% balance,
and so the (waived) interest on the 0% balance also becomes
un-waived etc.