Actually, this is not at all accurate. Military leaders had a quick reaction force standing by, which was thoroughly prepared and went in instantly when help was requested. One company of the 10th Mountain Division (an elite light infantry unit) was always on immediate call, with another on (IIRC) four hour call and a third training up but on 24 hour call. The 2d battalion commander was monitoring the fight (about which he was completely uninformed until it began) and had his first echelon as prepared and as briefed as was possible given his state of ignorance, and he got his second and third echelon forces operational well under his mandate. There were two major problems, one military and one political. The military problem was that, for operational reasons, the Special Forces contingent kept the UN and even the 10th Mountain completely in the dark as to where they were operating, the immediate operational environment, and the opposing forces. The political problem was that, to maintain the fiction that this was not a civil war, the DoD & White House denied the requests for armor and heavy air support. The net result was that, although a battalion of the 10th Mountain is certainly a capable combat unit, it was forced to make ad hoc arrangements with local UN armor to complete its mission of saving and evacuating the SF operators and Rangers. This was not at all a case of failing to make adequate contingency plans, but a case of those contingency plans being hampered by too-rosy projections (for non-domestic political purposes) and a combination of institutional jealousies spreading legitimate security concerns beyond a reasonable limit. That is quite different from using too-rosy projections (for non-domestic political purposes) as an excuse to have no real security and no contingency plans whatsoever. The one similarity is that in both cases, quite reasonable requests were denied for non-domestic political purposes and Americans died as a result.
Mogadishu is a good case though for the dangers of sending in a response without adequate preparation and operational knowledge. A quick reaction force not only has to be available and on call, it also has to be properly equipped and kept up to the minute on exact ground conditions. Send in a force that is not properly equipped and/or not properly prepared for the threat and the exact terrain and it may well become another element needing to be rescued, even if it's a whole elite US combat battalion. Once the initial failure is called due, there is a legitimate struggle between the moral requirement to send help and the moral requirement to not throw in more forces you cannot support. You don't leave Americans to die, and you don't unnecessarily send in Americans to die, but if you don't prepare properly up front, one or both of those terrible things is likely to happen.