Are there any major noticeable limitations to genome sequence compression methods that use reference templates?
The most obvious drawback of the reference template method is that if you use it, you've already analysed data.

Usually, you get data from wet biologists. They sequence samples and upload sequences to a server. Often an uploading process is already automated. If you sequence in-house, the data is already on your server. If not - biologists do not want to do an extra job. Moreover, if it is not a big project you do not have that much data that transferring and storing it is the problem. So you'll get the data as *.fastq.gz files.

Then you make QC, align reads and make an SNV-calling or expression analysis or whatever you want. Aligning and SNV-calling could be painful, complicated (Copy Number Variation, heterozygosity etc) and time-consuming. It is the problem. Resulting data usually is stored as Variant Call Format (VCF). Under the influence of CRAM and 1K Genome Project which uses it, VCF has been developed.