In tennis, just as in any sport, specificity is key.
The fact that the pros do something may or may not be relevant. The only thing they have to worry about is maximizing their game. As such the benefit/time ratio really doesn't matter, or at least not nearly as much.
For non-pros with a limited amount of time to spend on their tennis, the benefit/time ratio is extremely important.
If you have extra time available to improve your tennis, almost all amateurs would benefit the most by spending that time playing more tennis (assuming it's spent in a productive way). That's not always practical, so the next step would be to spend it doing something with the most direct translation to tennis.
Speed and agility play a much more important role than strength in tennis. They are also pretty easy to train, and improve rapidly in people that haven't specifically worked on them.
Foot speed drills (ladder, agility patterns) and speed drills (cone, pattern drills) directly translate into tennis performance. These increase not only your speed but your fitness if the timing is done right (staying close to the work/rest cycle found in tennis play).
Muscle imbalances are not inherently bad if it's comparing a worked muscle to a non-worked one. Tennis players have stronger arms/shoulders/chests/backs on their dominant side. Balancing out the other side does not reduce the chance of injury, and will not improve performance (and may actually decrease it).
There are some specific strengthening exercises that can reduce injury. The most common tennis injury (other than TE which is 90%+ technique) is a shoulder injury of the external rotators. These can be easily strengthened using simple exercises using elastic bands. These only take a few minutes a day.
A simple core workout, not using weights at all, may also help reduce injury. The link is a bit of a stretch, but there's at least a suggestion. Again, this doesn't require a lot of time, or any equipment (though a balance ball opens a lot more options).
Static stretching at the end of the day can help prevent injuries. Again, this only takes a few minutes, even 5-10 minutes at night can make a difference. It's important to note that you should NEVER do static stretches before exercise. That has clearly been shown to not only increase the risk of injury, but also decrease performance.
Lifting weights has not been shown to be beneficial in tennis (or in almost any other sport). If you want to swing a tennis racquet faster, you are far better off practicing swinging it faster than spending time/energy lifting weights. 'Strength' is a complicated thing. The actual contractile capacity of your muscles are only a very small part of it, and that's the only part you train when lifting weights. You train it all when you do the activity your training for. If you want stronger legs so you can have a more explosive first step, you are far better off practicing an explosive first step than doing squats.
Some (and by no means all) pros do lift weights at times during the year. But that activity is the bottom of their priority list. They are doing it because they have time to do it in addition to doing all the other activities that are far more specific to tennis.
Sports training is really a lot simpler than it's made out to be. Specificity is key. The less time you have, the larger the percentage of that time should be spent doing the sport itself. As available time increases, you then want to isolate specific aspects, and train them in a manner that is as close as possible to how it occurs when playing. This allows you to more easily overload these aspects in a way that may not be possible while playing the sport. In tennis this can mean non-tennis activities (such as ladder drills) or tennis specific practice (such as cross-court drills, serve practice, etc.). There's almost always time to add some easy injury prevention (in the form of strengthening, core work, static stretching) at night.
EDIT: Forgot to add that plyometrics are a great way to improve explosive strength (much better than lifting). You do not need a lifting base before plyometrics, but you do need to start slowly. Giving yourself 2 weeks to build to maximal force efforts is usually enough for the ligaments/tendons to adapt to the increased workload. You need to be very diligent though, most people get impatient spending days or weeks doing easy hopping. Even though it feels easy and pain free, the tendons especially need time to adapt before you subject them to all out efforts.
