The best strategy is the one that works for you and you feel comfortable with. BUT.... Your strategy is not really what I'd reccomend to someone I care about.
Downsides: You're likely creating more debt for yourself by allocating all your debt to one place, you'll be paying at least one fee to start a loan, closing cards doesnt look good on your credit, you miss out on the snowball effect.

Snowball Part: Say you get used to paying your minimums across all cards, once you pay off one card you'll get the feeling of having more cashflow sooner than if u consolodated all your debt. While it may feel more convienent to pay one payment, I would rather get the "One card down" feeling more often. I think theres a positive psychological benefit here.