I would not say that your idea is completely out of the world. As Alex Eisenhut said, that is a product category which a very reputable company tried to fill. And I would not fall for the same ideas as wizard69, as he was asking for about everything in instruments that he needs in one package.
As someone who often had to do non-trivial and intrusive testing away from a bench or lab, I could find uses for a dedicated 'logic multimeter'. And yet, your idea has some way to go..
Some thoughts on such an instrument:
1.) It needs more signals/channels. 4 might work, but I would rather go for 8.
2.) It would need a very sophisticated design for the input circuit in order to be both fast and robust enough. Logic thresholds need to be programmable, preferably over a very wide range. Imagine someone who wants to look at a parallel interface between an absolute rotary encoder and a PLC. Or a output from a PLC. There you have 24V logic, while inside a circuit you should be able to work with modern low-volt logic series.
3.) add a dedicated trigger signal output (BNC), so that the device could work as a word recognizer probe for non-MSO oscilloscopes or whatever.
4.) Looking at UART data by itself is (IMO) not very useful, if you do not have the possibility to set a condition which freezes the output and/or stores data. Also, you just display all data like it came in continuously. There is a need tor timestamping. Also, display format should be selectable. Also useful would be a loopback function.
And the really useful thing would be to monitor BOTH channels of a serial communication, while fulfilling the previously mentioned functions.
5.) concerning the UI, I would use a dedicated up/down control at the side of the display for scrolling etc. Maybe a wheel or a switch with two detents per direction. Then add a hex keyboard (+clear/enter) below the mode switch.
6.) The logic analyser needs much more functionality to be of any relevance. Timing between signals, pulse width, occurence of certain overlaps etc.
7.) If you want someone to take this up commecially, you have to think about a market. If you think of a mobile test aid for professional electronics, discard the servo thing outright. Add I²C. One possible baseline here is to look at the functions of serial testers and make one which can cope with all usual interfaces without additional converters. But then most users would want the mostly used connectors in the right pinout. But that could be a dumb part connected over the signal interface connector as an add-on box.
8.) The GPS simulator is not a bad idea, given how many applications use GPS for timing and/or location reference. You would have to include the 1PPS pulse, although. And make some arrangements to select/deselect sequences and introduce common error conditions (for example, number of satellites suddenly dropping).
Now those are only partial, unconnected functions and ideas which would have to be integrated anew. I think that it is very likely that you would need a faster processing capability, which could be a µP/FPGA combination. But of course, this drives up complexity and power demand.
And even for the instrument outlined, I can't guarantee that someone would take it up. I have seen fine ideas to be ignored and left to die, from hand tools to software products. Then youwould have been right to base it on your own needs, so that at least your time and energy isn't lost.
BTW, I own a HP Logic Dart and would miss it. While it is far from the outlined device, it is much more than a simple logic probe. It did help me several times.