It would be somewhat faster in C, but the language choice isn't what affects performance the most. It is usually more effective to perform various tasks in parallel, rather than waiting for each to complete sequentially as simpler init systems do. For example, sshd and httpd could be started at the same time, since neither requires the other to be already running.
There is no single "Linux boot sequence". Each distribution has its own; there isn't even a single thing they all have in common. It can be in C, Perl, Haskell, anything; the only requirement is that an executable named
/init be present in the initramfs, or
/sbin/init in the root filesystem.
/etc/rc?.d scheme is simply an extension of the Unix boot process of 20 years ago, maybe even 30 years. The earliest Unix systems were rebooted fairly rarely, so they would have a simple script,
/etc/rc or similar, that would be launched by init and start various daemons sequentially.
Even today SysV init is being used to start all such scripts, although the exact method may vary. Originally, a system would start all scripts in
/etc/rc?.d in order; currently Debian uses Makefile-style dependencies.
Some distributions – Ubuntu, Chrome OS, Fedora up to v14 – have switched to Upstart, which is written in C and is "event-based", allowing daemons to be started in parallel. Another init system, systemd, appears to be rising quickly in popularity – it is used by default in Fedora and OpenSuSE. It is also written in C. (Both systems still read textual configuration files to decide which daemons are to be started.)
Those distributions which still stick with SysVinit usually do it for "simplicity"; the most commonly heard  arguments appear to be about shell scripts being easier to maintain than equivalent C code (although said shell scripts consist of 90% copypasta), as well as a mortal fear of introducing additional library dependencies [subjective]. You can see for yourself in this, this, this and this discussion threads on the Debian mailing list from May 2012.
(Disclaimer: I'm a systemd user myself.)