Adi777 here is thought process as tool for you to figure it all out yourself:
Make some simple root categories to juggle compromises around. These could be audio quality, cost, size and aesthetics. Now put them into priority order for your current project. If it is small bluetooth box for kitchen breakfast moments the priority order might be size, aesthetics, cost, audio quality. For retirement livingroom dream system the order might be audio quality, aesthetics, size and cost meaning that the cost doesnt matter but it has to have very good sound.
You can try figure out what the commercial speakers have had in their priority list! If marketing material is plenty then its probably aesthetics before absolutely top audio quality, perhaps size and cost too if its a small speaker, but you have to figure out the market they are targeted to etc. Little bit of imagination and you'll start figure out at least some compromises they have.
Here is how it works. You got a problem, say how to determine how many ways system should have? If there is one way what are the compromises? How these fall on your priority list? Lets use the kitchen radio project as example. One way speaker is simple, cost effective, can be big or small, but has numerous issues on audio quality mainly with SPL capability and bandwidth extension. Well, thats fine for the kitchen radio, nice, suits very well for that project and its priority list! If it was a party system instead then the trade-off with limited SPL and bandwidth already rules one way system out and you should test if two way system would do. Put some numbers in to some calculators on the web and you'll probably end up three way system at least, for parties.
Then you'd just continue solving problems you encounter, navigating between options thinking their trade-offs referencing them to your priority list. If you manage to solve all questions / problems so that there is no bad compromise, a trade-off, in the main priority, IOW costly drivers on low cost system or poor SPL capability on party system, then you can count it as "no compromise system". Perhaps some problems were missed because of lacking knowledge but its a good start already, tons of learning with every project.
Important lesson here is that there is always compromises, trade-offs, and different applications benefit from different set of compromises taken. If you want best sounding speaker, no comromises on audio quality, then try and push all the trade-offs on design problems to aesthetics, size and cost and there you have it. Its probably big and ugly and costly system
it doesn't have to be if you manage to hide it and not go overboard with costs
Also, don't go excess because it might limit options on some problems later on. For example if three ways are enough for a party system dont go with four just because. You could though, if some other issues later on in the design process demand it for better compromises here and there. This in mind, take mindset initially that anything is possible, to keep all options open. For example do not buy fashionable drivers before you have a design fully thought out, because they migh be the wrong ones! Timing is fixable with DSP etc. Many many things, complicated soup, better have some process to navigate through successfully.