A launch site at latitude L can launch into an orbit of inclination L *or higher*. You can launch into a polar orbit from anywhere on the planet. You can only launch into an equatorial orbit from the equator. Equatorial sites have the advantage, not high latitude sites. (Also, the hemisphere doesn't matter. Something launched into low Earth orbit from 45 degrees south will be at 45 degrees north in about 45 minutes time.)
Yes, you can launch into one orbit then change plane to a lower inclination later - but doing so in LEO is very expensive. (I think the cheapest way to do it is to put yourself into a high eccentricity orbit, do the plane change at max distance from Earth, then recircularize your orbit into LEO.) ('expense' = delta-v.)
Launching from latitude L also can't launch into retrograde orbits closer than L to 180 degrees. E.g. from latitude +/- 30 degrees, you can launch directly into orbits with inclination between 30 and 150 degrees.
If you specifically want a 45 degree inclination orbit, I don't know whether launching due east from a 45 degree latitude is cheaper or more expensive than launching either NE or SE from an equatorial site. I suspect there is no difference.