It’s relatively straightforward and doesn’t take much force to bend a shape precisely out of wire, for example copper or steel wire; this can even be a complex three-dimensional shape, although you have to take into account springback and work-hardening. However, unless the wire is very thick (which makes it harder to bend) the resulting object is fairly weak unless the wires are then twisted together, which may not always be feasible. If you weld adjacent wires together, you can get a fairly solid structure, but this both distorts the overall structure as the welds cool and introduces surface positioning error locally due to surface tension.
Electrodeposition is an interesting alternative to welding in this context. It’s a terrible alternative to welding in the usual contexts, because material deposition at any given position is very slow, and you get almost no penetration into joints. But in the case of a wireframe structure, the “joints” may initially have only grazing contact or no contact at all, and it’s only necessary to deposit a thickness of material comparable to the thickness of the original wire to get a fully-strong structure. Even much smaller thicknesses of deposition may provide adequate strength for many applications.
Not only does the process introduce little or no side loading or distortion, but submerging the workpiece in water actually reduces the side loading resulting from the weight of the wire, though this is not very significant if the wire is a dense material like copper.
As Wolf Hilbertz discovered in 01976, cathodic deposition is significant even in seawater, where it results not in electroplating but in the precipitation of a hydromagnesite-aragonite stone due to the hydroxyls formed at the cathode; apparently he got about 5 cm/year (1.6 nm/s) with under 4 volts, though I vaguely remember the Mother Earth News article recommending 12 volts. If you get to choose the electrolyte you can do electrodeposition of metals much faster than that; presumably that’s true of these carbonate minerals as well. See Fast electrolytic mineral accretion (seacrete) for digital fabrication? for more notes on seacrete.
(Of course electrodeposition, either of metal or of stone, is also interesting as a way to add strength to aluminum-foil structures, including aluminum-foil origami.)