We present a first study based on the analysis of the DEep Spectra of Ionized REgions Data base (DESIRED). This is a compilation of 190 high signal-to-noise ratio optical spectra of $\mathrm{H\, \scriptstyle II}$ regions and other photoionized nebulae, mostly observed with 8-10 m telescopes and containing ~29 380 emission lines. We find that the electron density -ne- of the objects is underestimated when [$\mathrm{S\, \scriptstyle II}$] λ6731/λ6716 and/or [$\mathrm{O\, \scriptstyle II}$] λ3726/λ3729 are the only density indicators available. This is produced by the non-linear density dependence of the indicators in the presence of density inhomogeneities. The average underestimate is ~300 cm-3 in extragalactic $\mathrm{H\, \scriptstyle II}$ regions, introducing systematic overestimates of Te([$\mathrm{O\, \scriptstyle II}$]) and Te([$\mathrm{S\, \scriptstyle II}$]) compared to Te([$\mathrm{N\, \scriptstyle II}$]). The high-sensitivity of [$\mathrm{O\, \scriptstyle II}$] λλ7319 + 20 + 30 + 31/λλ3726 + 29 and [$\mathrm{S\, \scriptstyle II}$] λλ4069 + 76/λλ6716 + 31 to density makes them more suitable for the diagnosis of the presence of high-density clumps. If Te([$\mathrm{N\, \scriptstyle II}$]) is adopted, the density underestimate has a small impact in the ionic abundances derived from optical spectra, being limited to up to ~0.1 dex when auroral [$\mathrm{S\, \scriptstyle II}$] and/or [$\mathrm{O\, \scriptstyle II}$] lines are used. However, these density effects are critical for the analysis of infrared fine structure lines, such as those observed by the JWST in local star forming regions, implying strong underestimates of the ionic abundances. We present temperature relations between Te([$\mathrm{O\, \scriptstyle III}$]), Te([$\mathrm{Ar\, \scriptstyle III}$]), Te([$\mathrm{S\, \scriptstyle III}$]), and Te([$\mathrm{N\, \scriptstyle II}$]) for the extragalactic $\mathrm{H\, \scriptstyle II}$ regions. We confirm a non-linear dependence between Te([$\mathrm{O\, \scriptstyle III}$]) and Te([$\mathrm{N\, \scriptstyle II}$]) due to a more rapid increase of Te([$\mathrm{O\, \scriptstyle III}$]) at lower metallicities.