Out of curiosity, are you using Postgres with SSL for an offsite or multi-DC replica? Would switching to a site-to-site VPN be more efficient here?
And the VPN server may very well become a bottleneck for transfer speed at some point, but most of us won't ever need to deal with a level of bandwidth where that's an issue.
Site-to-site VPN would not have been an option in this instance, and in general I have had poor experience with them - Flaky SPOF, poor throughput, and so on.