As in the US there is a push to replace IBOR based swaps with SOFR rate does that mean that SOFR swap pricing will return to using a single curve framework as LIBOR swaps did pre the financial crisis?
I think the question was about dual curve stripping.
As much as I know, the market is using SOFR discounting for all sorts of quotations now. For example, swaption vol is quoted with SOFR discounting, CME and LCH moved to SOFR PAI and discounting on Oct. 16 2020 on new AND legacy swaps.
For EUR cleared, major CCPs did this since July 27 2020.
The market switched to discounting with the relevant RFR rates on the dates above. Hence, if you have a dual stripped curve (e.g. 3m US libor), you use SOFR and no longer OIS (FF).
ISDA fallbacks will apply from 31 December 2021 for GBP, JPY, CHF and Euro-LIBOR and from 30 June 2023 for USD LIBOR. Even if there were some synthetic or "zombie" Libor after it officially ceases to exist, it is expected that liquidity will drop significantly. Note that the FED have issued supervisory guidance encouraging banks to “cease entering into new contracts that use USD LIBOR as a reference rate as soon as practicable and in any event by December 31, 2021”.
Once Libor is gone, your major reference is RFR. As such, you do not have dual curve stripping. The only remaining "dual curve" logic should be having CME vs LCH stripped curves to account for the basis due to IM imbalances at CCPs in my opinion.