TIS,
Sorry for the delay in responding, I've been at work.
I can't speak to specifics at SoCal, I don't work there. Having said that, I know from having worked similar situations many times that there may be several mis-conceptions at work here. I won't get into all the details here, but suffice to say there are rules and procedures for parallel visual approaches, rules and procedures for parallel ILS approaches, and rules and facility SOP for ILS turn-ons. The rules don't change from day to day, but they do depend on the facility configuration and equipment in use at the time. In other words, a facility may not be set up at the moment for reduced separation ILS approaches. Requires extra controllers and scopes up and running. If visuals have been "working" for the most part, the facility may not have those sectors open at the moment. (If the WX is VFR, those controllers are probably at a satellite position, or somewhere else besides the breakroom...)
When the controllers are anticipating using visual approaches, they may not be feeding the finals in the same way they would for ILSs. So you get turned on a "base" and the controller points out a heavy on the parallel final and asks "can you see him?". You say "sure" everything works as planned. (and, as a side-note, from a controller's perspective, what could be easier to see than a B747???) If you don't see him, there may not be spacing or adequate vertical separation for a legal ILS turn-on for you.
At my facility, I can legally vector you toward the parallel final side by side with the heavy doing an ILS so long as you have visual with the heavy or your runway in sight for a visual. If you don't see the runway or the heavy, I now have to turn you on final 3-5 miles and/or 1000' from the heavy, and after you've gotten reasonably established, I can then reduce that separation to a lower value, again depending on equipment and tracon set-up at the time. But what if I've already got two or three more on the straight-in set up to follow you? I can't widen your base to maintain legal separation with the heavy without causing a conflict with the folks following you. Had I been planning an ILS turn on to begin with, I either wouldn't have tried to squeeze you into that hole, or I'd have built in more separation to begin with.
So, what I'm saying is that I've seen a situation very similar to what you've described many times, and if you don't report the heavy in sight, I will break you out from the base and re-sequence you for the ILS. It won't be "punishment" for not "playing ball". It will because there is no other legal option available. And I might even sound a bit testy at having my original sequence go to crap. If so, I apologize.
Having said all that, I have absolutely no problem with a crew that straight up asks for the ILS 30 miles out. I'll plan my sequence and spacing accordingly. Therefore I'm suggesting that if LAX is advertising visuals, and you don't ask for an ILS early, you *might* be contributing to the problem. It happens as I just described at lots of places. Nobody is "punishing" a crew that wants an ILS, but it requires more separation for the turn-on in many cases, and you might have to go three or more slots further back in the sequence to get that separation.
And, by the way TIS, I'll get my coffee break when it's my turn, whether you're short final or still on downwind 30 east....