No, they are not mandatory. Some applications like Digital TV broadcast, where tight synchronisation is required, will make an extensive use of time stamps. DTS and PTS time stamps are not relevant if reference time stamps are not present. They are inserted as close as possible to the portions of compressed video, audio, or data to which they apply. Precisely, this means that they are inserted in the PES packet headers, a syntax which is common to all data sources.
PSI has no synchronisation pattern in the section headers.
A PES packet is a way to uniformly packetize elementary streams. Embedded in PES packets, elementary streams may be synchronized with time stamps. They are not protected. The PES packets may be of variable length, which allows them to be also of fixed length. PES packets may be rather long packets.