There is no right answer to this. It also depends a lot on what type of music you are producing as well. For example if you are producing electronic music and you are using a variety of synths (hardware or software) I have actually found things can sound better when you use the built in reverbs/effects of many different instruments.
Earlier on I used to switch off a lot of built in reverbs/effects but I have found in many cases you want these parts to be more separate in nature. It helps to set them apart from each other and built in effects is an excellent way to do it. It will save CPU power too in the process.
All of the hardware synths I use feature built in effects. I have learned to program them more deeply and as a result they are all adding their own quite distinct character all helping to separate the instruments much more so. Especially once you start toning them way down too and put them back into subtle mode rather than swimming mode. Before you right them off spend some time playing and programming the effects to the max. Often you end up creating nice processing that may just surprise you.
Many people turn the effects off these things not knowing enough about the effects themselves. With some care and programming very effective effects can be applied within the instruments. In many cases the built in effects are
very integral to the patch.
(eg the chorus in a Roland Juno 106. You won’t get that effect anywhere, period) Take them off and they are gone.
But this may apply to electronic music for example. It may not work so well in an acoustic or rock track though. Then it may be better to switch a few of them off and put more than one part into a suitable effect or space as per the OP. eg to create the effect of several things being in the same space. It may work for some things but it can hinder other situations. You need to evaluate.
Some synths have killer reverbs and effects, way better than a lot of DAW effects too. And lots of em. There are 16 effects processors in my Kurzweil PC3K and 56 in the Novation Supernova II. Yes folks 56! And they sound bloody fabulous too. You would be foolish to switch these off!