Given the manner in which U.S consular services are organised it is no surprise that they have been hit by the imposed staffing cuts. From what I have seen the 'official' Russian reaction reflects an understanding of that. Of course there is inevitable noise making, but that's normal and to be expected. Outlets such as Russia Insider are bound to pick that up and amplify it, that's what they do!
In a similar situation Russia would be much less affected because they outsource most of the consular work related to visas.
I can understand the need to suspend the service for a few days given that all work is going to have to be centralised to Moscow, that will not be a small task to organise and implement just before most of the staff leave and hand over the work to a skeleton staff. Whatever happens I am sure that the U.S will absolutely not compromise on their consular protocols even if it causes significant inconvenience to tourists. I can not fault them in that regard, that's exactly as it should be!
Which mode of operation is most effective depends upon the needs of the country but it seems as though the Russian model, after some years of inefficiency, is now working reasonably well. The U.S system has always been very inconvenient for those seeking a visa to that country. So, on the whole, status quo applies.