Why is cell count stated relative to animal size? Why do some single-cell RNA-seq papers give the number of cells sampled as a fraction of the size of the organ, animal, or embryo, as opposed to just saying how many cells they sampled? 

For instance, Wagner et al.'s paper "Single-cell mapping of gene expression landscapes and lineage in the zebrafish embryo" says "For different developmental stages, we sampled 0.17x to 0.97x of the total cells per embryo, sufficient to detect cell states as rare as 0.1-0.5% of all cells." A pollster would never write "We sampled 4 out of every 10,000 registered voters in the USA"; they'd just give the number. Statistical results on cluster detection (e.g. Disentangling Gaussians by Adam Tauman Kalai, Ankur Moitra, and Gregory Valiant) are also phrased in terms of number of samples, not this ratio of sample size to organism size.

It's worth mentioning that these studies use low-yield techniques. In order to sequence 0.97 times the number of cells in a zebrafish embryo, Wagner et al. had to sequence at least 50-100 embryos. So, it's more like sampling 97 of 100 cells with replacement and less like sampling 97 of 100 cells without replacement.
The typical goal of scRNA-seq is to assess the possible cell-types and states that exist in an organism/tissue/etc. Given that, it can be useful to know what portion of the possible cells have been assayed, since that sets bounds on the number and size of cell populations not assayed. If the goal of a study is to assess the variability in a single cell-type, then you're correct that mentioning "0.8% of the population was sequenced" isn't actually informative. Note that "in a single cell-type" is important there, since if one is assaying multiple cell-types then it's important that enough of each are assayed given their prevalence in the relevant population.

Practically speaking, numbers like this are only ever written in papers if they look impressive, so no one is going to write about sequencing 0.000001% of the cells in an organism, since the reader/reviewer will then start to question the relevance of the results.