As y increases from ``tiny'' to ``standard,'' the cost of sieving drops down to a smallest possible value, while the cost of linear algebra rises. As y increases past standard, the cost of sieving starts rising again, and keeps rising, while the cost of linear algebra also rises.
That claim is obviously false. One can always decrease y to reduce the cost of linear algebra until sieving and linear algebra are in balance.
Section 4.3 of the June 2002 Lenstra-Shamir-Tomlinson-Tromer paper says that ``in past factorization experiments'' linear algebra was never a bottleneck. This is a content-free observation. Linear algebra is never a bottleneck.
That claim is also false, at least for large numbers. (It is true for Pomerance's optimized version of conventional NFS, but circuit NFS is much more cost-effective than conventional NFS for large numbers.) As stated in my October 2001 grant proposal, the optimal value of y for circuit NFS is substantially smaller than standard, so one can increase y to reduce the cost of sieving until sieving and linear algebra are in balance.
Perhaps someday we'll discover better linear-algebra methods. Perhaps the cost of linear algebra will become unnoticeable for standard values of y; then sieving by itself will be a bottleneck. However, as stated in my grant proposal, the current situation for large numbers is that linear algebra is relatively difficult; as a consequence, when parameters are chosen properly, sieving and linear algebra are in balance.