It's not cost-free. It comes at the cost of greatly increased latency. 29.9 seconds per token with Llama 3.1-70B. This is from Table 1 (pg 8) of the paper.
The actual goal of the article is to highlight that we can optimise the overall speed by decreasing link latency. Yeah link latency, because it's not 1 machine but several low devices that are used together to serve the 70B LLM.
In other words, if I want 100 tokens of output, do I have to wait 2990 seconds? If so, the terminology seems unnecessarily confusing.
For vanilla models, you always use all the weights. That isn't true for mixture-of-experts, though, and in that setting, your approach has merit.
The number of layers, and the amount of time spent in each of them, makes me think any benefit from pre-loading the layer ahead is negligible.
You really need the entire model on device to consider it performant.