Have you actually tried to get your LBS to price match Online pricing? If you succeed in that, then you'll actually be costing them money rather than supporting them, according to my range of LBS. That includes both a single small shop owners, and also a chain that is known nationally. Neither of them can buy in at the price that online companies sell for.
Really it depends on the item. Sometimes they might just say no. I just ordered a set of Schwalbe G-One Evos at my shop, I might have paid a couple of quid more than the absolute cheapest online, but I don't have to take a chance on some shop in the middle of nowhere. When ordering online from unknown entities there's the worry about warranty returns and cost of postage or, not to mention the faff with the royal mail collections office queue, as inevitably you're out when it arrives. I have found wiggle and
CRC great for returns, but they are not always the cheapest.
You're right though, if you can manage a price match, LBS margins will be miniscule if they price match the cheapest retailer, most don't go that far, but do match the likes of wiggle, CRC and evans. Those that do actually really rely on your return custom when they do this, i.e. bringing the bike in for repairs and service. Aside for charging for labour, most independent mechanic run shops probably make most money on their builds and labour. I imagine they won't do this with every tight arse that walks through the shop, and only the savviest have the nerve to ask. I've found to get the best deals you'll need to build a bit of rapport with the owner first, not hard to do if you frequent the shop. After all you can't haggle with wiggle!
I wouldn't be price checking an entire custom build I had commissioned with them, I do that work myself anyway. I've been told by other shops it's not worth their effort to price match an entire list of parts for a DIY bike build, but I presented a list of items I intended to buy online and asked them, what if anything they can do cheaper than I had on my list from their stock. I ended up buying a nearly new (used) stem, a new bottom bracket and headset from them, all fitted, and they had to have a healthy margin on those, as they were just regular priced items, no flash sales. The likes of wiggle and CRC don't always have the slimmest margins that people imagine, and big centralised warehouses and just in time delivery of goods has their own hidden costs, ones that LBS don't have to worry about. Warehouses and pickers aren't necessarily cheaper than an LBS. Lots of variables though.