It does seem like the overcrowding on long distance services was at just about its worse this weekend.
A Tweet on the LNER feed caught my eye, in response to customers complaining about the busyness of services:
If you look at the LNER feed over much of the weekend, there's a lot of blaming busyness on flexible ticket holders. While this is just a Twitter team, there's a clear sense from multiple TOCs that they'd find a long-distance reservation system preferable in many ways. So I don't think it's just in Virgin that these views are held.
That said, I don't think we're likely to see anything like this introduced on a widespread scale across the rail network any time soon: it doesn't fit with an integrated network, with moves to encourage commuting, with people's expectations, etc. I wouldn't be surprised if one way of coping with engineering work in future would be to introduce reservation-only days though.