Browsers depend on tons of 20-year-old C libraries. At the moment, the top link from the Twitter account you gave above is this one from November 6: https://twitter.com/LazyFishBarrel/status/119228101802954342...

It reports a total of 37 issues in:

  - freetype2 (C lib, 20+ years old)
  - usrsctp (C lib, age unknown)
  - libexif (C lib, age unknown)
  - libxslt (C lib, 20+ years old)
  - imagemagick (C lib, 20+ years old)
  - mruby (C)
  - php (C)
  - openSSL (C, 20+ years old)
  - curl (C lib, 20+ years old)
  - ffmpeg (C lib, 18 years old)
  - ghostscript (C lib, 30 years old)
  - irssi (C, 20 years old)

In that list were also Skia and libsass, two projects actually written in C++.

In Sass, the issue is a nullptr issue: https://github.com/sass/libsass/issues/3001

In Skia the bug was in intrinsics code: https://skia.googlesource.com/skia/+/0f55db539032a23b52897ae...

Of course that's a single data point, but it shows what I think is a reasonable argument: most of the issues indeed happen in (old) C code, for well-known reasons (no standard string, array or collection support, no RAII), but because C++ supports those things by default it largely avoids those issues.