I have never worked in the private sector - only education, and government (or for international bodies).
Thus far, the discussion on dating has focussed on firstly, the possible negative effects for others (as expressed so well by @GrumpyMom - and I have seen this played out in practice) if one party of the happy couple dislikes a subordinate, 2) by the perception - as mentioned by several - that the junior partner of the subordinate couple may be considered to have been the recipient of unfair favour, and 3) as correctly pointed out by @yaxomoxay - if and when the happy couple fall out, the damage they can leave in their wake - especially if jointly they allowed abuses of power or authority to exist - can be considerable. (This, too, I have witnessed).
There is a fourth dimension which I have seen also play out in some international contexts and it is this: An individual holding a senior position - usually male and middle aged, or older - seeks to date a (younger, female) subordinate who reports to him. (And I have seen that one play out, too). In truth, it is exceptionally difficult for her to turn him down, not without adverse repercussions.
I agree there are many problems / issues with the dating within the company and it almost always turns out bad.
I was only questioning if companies really try to restrict your actions outside your working hours by listing dating restrictions in the HR manual. Is it even legal for them to do so ?