With the midi sized lathes I have found that the cheaper made Asian brands work pretty darn well. This is mainly due to the scale of work being done allowing them to serve their basic function. Like the midi lathes category, the chisels don't have to be name brand.
For larger projects where you have larger chunks of wood and potentially more tool reaching beyond the tools rest I do with known quality tools. The catches that can happen are more violent and stressing on the tools. Cheaper steal is more prone to break and when combined with longer reach that can be a potentially dangerous situation. For me, I save up my pennies and get one larger tool at a time or watch forums for people selling off used ones. I have gotten most of my larger tools this way. Quality tools do make a difference once you start moving up in sizes.
I am also not a fan of the tools multiple attachments and only one handle size. You should have a handle for each tool, granted you can make them. Another option is getting handles of different lengths to allow work in different scenarios and you can switch tool heads between handles as needed.
Thompson tools, Carter and Sons, Robust, Ashley Harwood, Oneway and D-way have a variety of handle sizes. I have a variety of handles from D-way for interchanging chisels, their size, weight and durability are a fit for me. Plus the D-way knob for tightening makes it very quick and easy. There is a cost but you get a lot of versatility with the handles. Getting different designed tools rests can go a long way as well.
All of that to say, I personally don't recommend the cheap and generic made in China tools of amazon or from anywhere else for the large turning tools.