I think that keeping the old dm-eri contraction could be better.

This is mostly for efficiency concern when density matrix is not low-rank enough. Assuming that we have to dealing with DF-K integral,

• SVD is some $O(N^3)$ which is ignorable if BLAS is efficient enough. Given rank of density matrix $n_\mathrm{rank}$, then there are two ERI-DM GEMM contraction steps (both $2 n_\mathrm{rank} n_\mathrm{basis}^2 n_\mathrm{aux}$ FLOPs), and one GEMM contract step to give the final K matrix ($2 n_\mathrm{rank} n_\mathrm{basis}^2 n_\mathrm{aux}$ FLOPs), so in total $6 n_\mathrm{rank} n_\mathrm{basis}^2 n_\mathrm{aux}$ FLOPs.
• Old dm-eri requires a first step to perform ERI-DM GEMM contraction ($2 n_\mathrm{basis}^3 n_\mathrm{aux}$ FLOPs), and then contract to another ERI ($2 n_\mathrm{basis}^3 n_\mathrm{aux}$ FLOPs), so in total $4 n_\mathrm{basis}^3 n_\mathrm{aux}$ FLOPs.
• So, theoretically, only when $n_\mathrm{rank} < \frac{2}{3} n_\mathrm{basis}$, then the computational cost of SVD can be smaller than old dm-eri contraction. In other words, if density matrix is in full rank (like density matrices in post-HF), then the computational cost actually arises when using SVD. But if density matrix is from SCF or SCF's derivative (when evaluating hessian in SCF), the cost can be reduced due to $n_\mathrm{occ} < \frac{2}{3} n_\mathrm{basis}$.

I believe that this technique may not only be applied to non-hermitian density matrix, but could also applicable to sy/he (symmetric/hermitian). However, most sy/he cases has already been optimized by passing tagged ndarray dm.mo_coeff and dm.mo_occ to DF-JK veff function, so I think that perhaps it may not be that necessary to change sy/he code in PySCF.

Also, I think that this topic is related to building DF-JK with different left (bra) and right (ket) coefficients, something similar to Psi4's DFHelper::build_JK.