While troops aren't working most weekends, my experience the last number of years and based on this year's training calendar is that most leadership is working at least half, and often the majority of weekends as is. There physically aren't more NCOs to run additional training on any weekends that are actually free, which isn't many of them. Off the top of my head we're running 4 courses, and supplying instructors for 2-3 more. Some of these courses are fortunately short, and can combine things like ranges, but it gets impractical to ask people with families and civilian careers to start sacrificing every weekend for most of the year, before even getting into asking them to try and take a month/two/three months off to teach summer courses on top of that. This will obviously vary by unit of course.
I like the idea of more weekend training vs weeknights as you get more training value out of a whole day on say, a Saturday, rather than a couple weeknights, but unless we have a robust training establishment that can take care of all the weekend courses, and focus unit leadership on regular unit training it's extremely difficult, if not impossible, with current demands on what leadership is still around, outside of the occasional event.
Some weeknights are wasted, but there are plenty that are useful, battle procedure for exercises, post-ex drills, covering the myriad annual training requirements we need to hit, etc. Even with weekends being more efficient, a unit that isn't planning and effectively using it's weeknight training time is probably going to suffer the same failure to plan that will to lead to poorly utilized weekends and exercises in general.
Re: roll call and paysheets, roll call should be quick, but we desperately need a better system than pay sheets. That said, at least everything I've ever done, paysheets are signed before parade begins, so it shouldn't cut into the actual training time.
Tactical grouping of units can also help alleviate some of the above issues, but while some of the best exercises I've done were multi-unit exercises in the early 2010s, the last time we did a bunch of multi-unit exercises it was a disaster of lack of planning, communication, and conflicting priorities and directives from seemingly everyone involved. Also groupings should be based on logical parameters, like say, geography, rather than whether or not units wear funny hats.
We're missing a lot of things, and critically short of what we do we have, but even then it can be managed effectively, it just requires cooperation and good planning, the latter of which seems to be chronically missing.
Evenings are not an efficient use of paid time. Changing culture to weekends-only will likely have short-terms costs (eg. retention) but long-term would likely be better for the institution, as would shifting days out of the Sep-Jun frame to create an additional one-week summer block (ie. a two-week concentration).
I think the two week summer exercise hits the sweet spot for minimizing disruption of member's civilian obligations, while offering a good chunk of time to get good training in. Three weeks of training time is great, but starts getting more difficult depending on the employer. Align annual training plans to the concentration ex and even with our limited resources you can achieve good results.
None of this helps the support aspect, such as maintenance space, parts, tooling, training techs, or letting techs do tech things, but I'm not a tech and can't meaningfully comment on that outside of give them training, tools, spaces to work, and let their focus be on fixing stuff.