If I understood JFET diagram correctly, the p-n junction is only used to isolate gate. Using same principle, would it be possible to construct a MOSFET with no junction at all, i. e. a single semiconductor type transistor?
The answer to your question is yes a single N or P type depletion mode mosfets can be built. If you do a search on TFT transistors you will find how they are use in LCD displays. This is from a my solid state devices text book, which is very old;
Usually depletion mode mosfets are built on a substrate of the opposite type of material. That is because it is easy to do with current fabrication methods. The substrate is not needed for the opporation of the device.
would it be possible to construct a MOSFET with no junction at all, i. e. a single semiconductor type transistor?
The above is for a P channel JFET as linked in the question.
The gate source region needs to form a depletion layer so that the P channel can be progressively cut-off thus restricting current flow from source to drain. Without the N type material at the gate, a depletion region cannot be formed therefore you cannot control the drain current other than by brute force; taking current away from the source (via the gate) that would otherwise get to the drain.
That's not a transistor any more as far as I see it.
would it be possible to construct a MOSFET with no junction at all
No because it is the reverse biased PN junction which provides the isolation needed to turn the device off, meaning no current can flow.
A single bar of N or P type semiconductor in general behaves as a resistor. Certain types of on-chip resistors are made this way.