I am of the same opinion. It just seemed like common sense to me that incandescent lamps are just heaters which give off some light, 10% light and 90% heat, so if you change to LED, 60% light 40% heat (that's overall efficiency) you are reducing the amount of heat produced. If the house temperature is controlled and remains the same, the CH will have to supply the difference, so savings will be minimal.
In a hotter climate, it's a different story, there would be a bigger saving because the air conditioning would run less to remove the extra heat from the incandescent bulbs.
I did some calculations on my usage and the total power consumption has gone up slightly, converting everything to LED. The reason is, I have much higher lighting levels in and around the house with incandescent, 21500 total lumens for Incandescent and 64700 total lumens for LED.
I'm not suggesting we go back to incandescent. I love LED lighting, but they didn't give the whole picture. I would like to see how much energy it takes to make an LED bulb compared to incandescent, the whole life cost of both, including disposal and recycling.
You raise a number of intersecting points. firstly with LED you have added more light, it is more affordable so we use more, that is always a problem with advances in technology, they tend to increase consumption. Our household is the same, my wife and I need a lot more lumens to see than the kids so we have increased the number of lumens in the home with LED and also added a lot more outside lights. That said, LED use 10x less electricity than incandescent so you are still winning, I'm surprised you electricity bill hasn't fallen, I'd expect you lighting to use on 1/3 of the electricity of the incandescent even at 64k lumens. Maybe they are left on longer? or the kettle or washer dryer, which are the dominant users in our household have outweighed the light saving.
Overall LEDs have reduced the world's office electricity bill by 25% that is a lot of CO2 saved. Its a genuine win win, less CO2 and less cost.
The other question you asked was life cycle analysis of LEDs vs Incandescent bulbs. In this case LEDs win hands down:
1. Firstly they use 90% less electricity whilst running and that is by far the biggest impact on the environment.
2. Secondly they last longer, on average about 15 times longer. Some last 50,000 hours, but although the semiconductor will last for 50,000 or more hours its usually the ballast that gives up, anytime from 10,000 to 25,000 hours. So you need 10 to 25 (say 15 on average) times more bulbs for one LED.
3. Finally LEDs use less harmful materials. They use a small amount of semiconductor (silicon, Nitrogen, gallium Phosphorus) and quite a lot of aluminium in the heat sink, but aluminium is 100% recyclable. Incandescent are made with glass which uses heat to form and also contain tungsten which is a scares metal, although Gallium is also a metal that is getting hard to source. The amount of gallium in a LED is tiny 0.025g vs 1g of Tungsten in an incandescent so gram for gram there is 400 times less rare metal. However even at these low concentrations, people are beginning to look at ways to recycle the metals. I should add a CFL contains 0.004g of mercury, not enough to harm us if one breaks but another win from switching to LEDs.