Chip-seq down-sampling problem
No, downsampling in general has no use as it reduces power. Peak callers such as macs2 will internally scale data to account for sequencing depth differences.
The IgG itself is only useful for peak calling as it somewhat corrects for the unspecificity of the antibody to precipitate any kind of protein rather than the protein of interest. I hear people say, and personally agree with this by experience with my own experiments, that of course IgG pulls down notably fewer DNA that the target antibody, therefore the library requires notably PCR to produce enough material for sequencing. And this then makes it questionable how representative IgG is as a control. I personally prefer chromatin input to account for the intrinsic sequence/GC bias of the underlying genomic region in the sequencing/mapping. To my knowledge there are currently few established tools to really take these controls into account for downstream analysis such as differential testing via interaction terms because the library composition is simply so different from the IPs making normalization difficult.
Your focus imho should be rather to properly normalize your samples to correct for differences is signal/noise ratio, see for example my post over at biostars on how one could do that beyond naive per-million scaling.