The idea that the DC-10 had a very bad safety record is somewhat of a misconception. The DC-10 did suffer from a number of high profile accidents, "high profile" being the key word here. Although the DC-10 did get its unequal share of blame for the AA crash in ORD, ONLY the cargo door latch mechanism emerged as a real design flaw that was safety related- this caused the crash of the THY DC-10 in 1974. When you look at the entire fleet of DC-10s (446 produced), the hull write-off rate is consistant with that of the 747 and only recently have DC-10s been retired in large numbers, before about a year ago the percentage of the 747 fleet that had been retired was about double that of the DC-10. For many years the DC-10 was neck and neck with the 747 in sales until the mid 80s when the 747's continued development (-300, -400) pushed it ahead in technology, thus sales.
The L1011 is widely regarded as the safest and most technologicaly advanced aircraft of its time. Its safety record was better than the 747 or DC-10 and it incorporated many fautures that were not found in the competing products for years. The L1011 suffered from both the lack of further development and the lack of a commercial airplane line from Lockheed aside from the TriStar. As much as operators liked the plane (and they did), they knew that the TriStar was their only choice from Lockheed, thus fleet comonality with one manufacturer was not possible. The TriStar, despite being a standout preformer is now dissappearing fast as the 250 fleet is down to only about 75 flying aircraft.
The issue with available engine power as noted in the post above certainly did not come into play until well into the late 80s. The large diameter turbofans developed for the 777, A330 and 747-400 were not around in the 70s or early 80s and the trijet was still a logical niche through the 80s. The largest engines available were the JT9D, CF6 and RB211 all of the which the DC-10 and L1011 used. It was not till the MD-11 that the larger engines became an issue. The MD-11 was truely the pinnacle of trijet technology and when compared to the 777, 767 or A330 has advantages and disadvantages. The MD-11 can carry more cargo than any other freighter aside from the 747. It also has a very large belly capacity for cargo, larger than any other widebody. When you compare cargo lift, the MD-11 to the 747-200F can move the same amount of cargo for about 30% less cost in fuel and crew. The MD-11 still represents the most efficient, longest range freighter available and turns out to be perfectly suited to freighter duties, ye Boeing still shelved the project in favor of................leaving the segment empty.