I think that you will likely just cause issues for your players with such a simplistic solution. Many problem spells (e.g., haste) still exist and are still as viable as ever. However, many spells will be terrible now especially those that were borderline at the outset (e.g., damage spells).
However, some of the unexpected consequences include a direct reduction, across the board, to spell DCs staring at level 3-4 when full casters are not casting 2nd level spells. This means that casters either need to focus resources (feats, class abilities, magic items) on boosting their save DCs or they will quickly start seeing everything saving against their spells. This means damage spells (outside of a few exceptions like scorching ray), debuffing spells, and control spells will all become much more difficult or impossible to use effectively, especially when it matters. Casters will dominate mooks and be worthless against legitimate challenges.
I recommend banning full casters over your option. However, as Mad Master mentioned, it is much more effective (and time consuming) to go through the spell lists and edit troublesome spells. You will likely find that there are actually only a few problem spells. I also recommend limiting to a few core books (CRB and APG initially) then expanding the set very slowly and methodically as you are more comfortable with casters in your party.
TLDR: Directly converting full casters to 6 lvl casting progresion is probably going to kill their viability (and player fun) outside of a few options that will (likely) be minimally affected by the change. Taking the more methodical and time consuming approach mentioned by Mad Master above is a better option. Also, limit source books to a small set (CRB and APG) then expand slowly as you (the DM) grow comfortable with adding options.