There are many options today but the pictured connection is one of several valid wire to wire splice approaches including side by side and T splices. The wires must be clean (electrical), wound as shown (mechanical). A covering provides insulation, protection from the environment, and possibly additional mechanical support. If the splice is pulled or subject to repetitive motion (flexed) it could loosen. This would lead to loss of contact and oxidation.
At low voltage almost any tape would do for insulation. The problem is most tapes do not age well because the adhesive drys out or oozes or the tape itself deteriorates. Also, a failing splice on a high current line would get hot and affect the tape.
If you are going to use heat shrink or spaghetti, be sure to put the piece on the wire BEFORE you make the splice.
Never intentionally use Fahnestock clips for any purpose.