You're talking about a number of different things here. But first off, using your Sony HLV flash off-camera with your pop-up as master is a different system than typical "optical slaving." While this is optical and light-based, it's a proprietary signalling system that uses a series of light flashes to communicate information (which is why this system can support TTL, HSS, and remote power control), rather like morse code light blips. This is multiple pre-flashes, and that will typically make this system completely incompatible with any other "dumb" (manual-only) optical slave system, like the one you'll find on most studio strobes/monolights (which is what I'm interpreting you mean by "strobes for umbrella/softboxes; speedlights can use umbrellas and softboxes, too, y'know and also classify as strobes).
However. Nearly all monolights, even the cheap Chinese ones, typically come with a "dumb" optical slave sensor in it. It's rarer to find them in speedlights, but quite a few of the 3rd-party manual-only flashes incorporate them, too. This basically works as a sensor that turns a fast bright light pulse into an electrical signal that sets off the flash. The only signal it can convey is the "fire" signal, so it's a manual-only trigger. And it can be tripped early by any pre-flashes, although some of these slaves are now built with a way to fire on the second flash it sees, so it can use a master flash signal that's TTL with a single pre-flash (i.e., in whatever flavor of TTL your camera system uses, but NOT in "wireless master/slave" mode, which would emit multiple preflashes).
The drawbacks are the usual ones with any optical triggering system: range, line-of-sight, and being overpowered outdoors. The sensor must "see" the light signal. If there is anything blocking the master signal from the sensor panel, the signal won't get through, and it won't fire. Outside in bright sunlight, the signal might be overpowered and not register highly enough over the ambient light, and the signal is lost. And if the master signal is very far away, again, the signal might be lost. These triggers work best in studio conditions, where there are bounce surfaces to relay the signal if there's no direct line of sight, and where the master flash pulse will be considerably brighter than the ambient lighting.
This is why we like radio triggers; no line-of-sight requirements (just a lack of radio interference), and the range and reliability are better than with optical slaves--especially outside in the daytime.
Studio strobes also typically do not have PC sync ports--these days they mostly seem to use 3.5mm headphone minijacks/plugs to convey the sync signal.
See: Strobist posts: A walk around the Monobloc, pt. 1, and pt. 2.
