Have you checked to see if the outages are localized to specific areas?
I use Pingdom aswell and find that sites that show as down, only tend to be down for one or two locations, which I don't target anyway, but that's beside the point.
Dreamhost probably don't support self ping testings because;
1) Ping requests are generally given a much lower priority than other traffic on a network and may falsely return down.
2) (per my point above) Servers may appear to be down to specific locations due to circumstances outside of DreamHost's control, such as a line break, or service error - but internally will be operating perfectly normally / or available to other areas without issue.
3) Dreamhost (as with other hosts) may not offer pulse checking because there are dedicated solutions already available - why reinvent the wheel?
That aside, I do understand where you are coming from, I have in the past sent a number of frustrated support tickets to have an apache service restarted because one or more services are too slow or unavailable. This though hasn't happened too recently so I'm content to leave things be, but going forward I may seek a more powerful & reliable service else where.