There is nothing new about this. Putting a proxy into to modify content is as old as the usage of tcp proxies. What is new here is that they have no shame -- I don't expect software from a reputed company to pipe my email through their servers.
LinkedIn: moving their content to your e-mail address.
G-mail/Yahoo: Duplicating your content.
LinkedIn: Manipulating your content.
G-mail/Yahoo: E-mail providers.
LinkedIn: Social media provider.
G-mail/Yahoo: uses protocols as intended to provide service.
LinkedIn: uses hacks to provide service.
G-mail/Yahoo: No risk of compromising devices.
LinkedIn: Extreme risk of device compromise. Intentionally circumvents device security features. Multiple potential points of security breach (at proxy server, at web server, through rendering engine).
No comparison, really.
The only relevant difference is security/privacy, in which Google may be more trustworthy but even that is debatable, regardless of which side of the debate you land on.