I am sorry you found Groupy disappointing.

The reason we do not use the ctrl + hotkeys is simple, other applications use them and we would break things.

For example : Ctrl + tab in excel switches between workbooks, ctrl + tab in paint.net switches between documents and of course web browsers likewise.

If Groupy used those keys then any time any of those apps are grouped we would be disabling functionality in them.  This is why Win key is used complete with the key ABOVE tab.  It is an unused keyboard shortcut that's easy to access.

It is one thing to enable them on a single application you know does not use them (see Clover), it is an entirely different thing to enable them over everything when you have no idea what hotkeys an application might use.

Regarding the line, that is an optional setting (you can disable it from the main page in Groupy settings) which keeps visual consistency when you are switching between tabs above and tabs integrated modes.  It also gives you a place to drag the window and keeps things the same when maximized and non maximized.

To open a new tab you can click on the ... drop down menu and pick Always show Show Add tab button.  This is only enabled by default for some applications as not every application can open a new instance of itself.

On the design, I am afraid that's more of a personal choice thing.  We have not had complaints over that and we chose to follow the OS style for tabs and match in with Microsoft edge / IE and future Microsoft tabbed products.  The Google Chrome design typically works best with a space above the tabs and that would require invasive modifications at runtime to applications that could introduce compatibility issues.

That said we are open to providing different looks for the tabs in the future, but basic functionality was considered more important to start with.