The conference championship games will stay because they are a huge part of the TV Contracts and bring in millions of dollars in both TV revenue and gate for the conferences.
The reason they have always existed is primarily to increase the revenue for the conferences.
The new CFP is basically designed to get the conference champions from the P5 (and the top ranked G5 champion) team and then the next 6 highest ranked CFP teams.
If you used this week's CFP rankings and assumed the conference championship games are all won by the higher ranked team than a 12 team playoff this year would be (listing the conference champions in CFP order first and then the top 6 remaining CFP teams)
1.UGA -CFP #1, SEC Champ
2. Mich -CFP #2, B10 Champ
3.TCU - CFP #3, B12 Champ
4. USC - CFP #4, PAC Champ
5. Clemson - CFP #9, ACC Champ
6. Tulane - CFP #18, AAC Champ
7. Ohio St - CFP #5
8. AL - CFP #6
9. TN - CFP #7
10. Penn St - CFP #8
11. Kansas St - CFP #10
12. Utah - CFP #11
Washington and FSU would be the first 2 left out.
I believe the idea for the 12 team is that the top 4 get buys so I believe the structure would be
1. UGA - Bye
2. Mich - Bye
3. TCU - Bye
4. USC - Bye
5. Ohio St - 12. Tulane - winner plays USC
6. AL - 11. Utah - winner plays TCU
7. TN - 10. Kansas St - winner plays Mich
8. Penn St - 9. Clemson - winner plays UGA
I'm pretty sure the 12 teams picked will be seated based on their CFP rankings, not whether they are conference champions.
Clemson, Utah, and Tulane would be the only teams that would be in danger of missing the CFP with a conference championship game loss.
Clemson would be replaced by UNC (who would likely be the #12 seed, might be the #11 seed ahead of the G5 conference champ)
If UCF beats Tulane in the ACC Championship game they would get the G5 bid.
If Utah loses to USC then the committee would have to decide whether to keep them above Washington or move them behind them. Would be an interesting decision as dropping them would effectively be punishing them for playing in the Championship game, so there may be reason to keep them where they are.