Unless you have booked a technical dive trip, decompression diving, diving deeper than 40 meter is not allowed. This has to do with the permit, insurance, liability and possible resources. If you really want to go deeper and longer, you will have to book a technical dive trip.
So that means that the liveaboard normally organizes dives in the context of recreational diving, that you dive within the no-stop times, stay within 40 meters and make safety stops. Many people like to get the most out of all their dives and prefer to go as deep and as long as possible. But the question is why would you do that? You’re only tempting fate, and if you think that as long as you’re diving inside your computer’s no-stop times you’re safe, you’re not the first to be seriously mistaken. We have all learned that diving involves certain risks and when you do as many dives as you would on a liveaboard trip, the likelihood of those risks increases. So make your safety stop, stay well within the no-stop times and only go deep if you can see something special there and you are trained and certified to do so. Are you tired, then just skip a dive. If you have ear problems or problems with equalizing, take it easy, it can only break once and there is no dive worth it.
The dive computer and making safety stops are not a choice, but an obligation. Everyone should have a working computer and everyone makes the stops.