Several years ago we managed to convince the SE team to remove the 2 link limit for new users on Skeptics. This limit was particularly frustrating on this site, as any answer without links was likely to violate our reference rules, but new users couldn't put in more than 2 links. While there are workarounds, new users don't know them, and they were frustrated by these contradictory requirements.
Since this limit was removed on Skeptics, I can't actually remember ever seeing any spam with lots of links in it. Or any noticeable increase in spam volume in general.
The experience for new users on Stack Exchange sites is often marred by a large number of seemingly arbitrary rules we impose on them. Many of them have very good reasons behind them, even if those aren't immediately obvious. But I don't think the link limit is one of those.
One aspect that changed in the meantime is that there is now a community-run project to detect and remove spam (SmokeDetector). This makes it easier to observe the impact of any such change, and could also help to contain small increases in spam, if this change would cause them.
Stack Exchange has been trying to improve the new user experience for a while. And while this is probably only an issue for a small number of new users, I think it makes sense to evaluate or get rid of such small barriers for new users.