Even for pure text data, if a previous field was over-read (the only plausible way to have start-truncation), then you probably are decoding incorrect data from then on.
IOW, this upside is both ludicrously improbable and much more damning to the decoding than simply be able to skip a character.
10000011 11101001 U+E9 "é"
10000001 10000011 11101001 U+10E9 "ჩ"
This would make it incompatible with many existing processes that already handle text, which was one of the goals of UTF-8.With a code like this, your dumb terminal can be built so it just automatically works. Without it, the terminal may be off by some number of bytes, and you have to have some sort of other (probably manual) synchronization procedure.
Similarly, imagine you've dialed in over modem to a remote system. You get some errors or lost text due to noise on the phone line. Or some bytes are lost due to bad RS232 flow control or no flow control. Your terminal emulator would be able to recover.
There might also be uses where text is broadcast, such as in TV closed captions, although maybe those have their own framing so you know where strings begin.