It depends on the chord progression. If the chord progression implies a key change then you'd also change the key of your solo melody. In all other cases, you wouldn't change the key of your melody.

You gave a I-IV-V progression as an example. If you were to use the IV-major scale over the IV chord, you would make that chord sound like a new I chord, and not like the IV chord of the current key. The same is true for the V chord: by playing the V-major scale over it, it wouldn't sound like a dominant chord of the actual key; however, it is usually intended as a dominant chord leading back to the I chord.

Things are different if you have a modal piece like So What by Miles Davis. In the solo section you have D dorian (Dm7) before changing to Eb dorian (Ebm7). The Ebm7 chord does not function in the key of D minor, but it is something new. This means that in your solo you would change scales from D dorian to Eb dorian, simply reflecting what is happening harmonically.

Another different case is the blues. A basic I-IV-V blues is based on dominant seventh chords. There is no single chord scale for those 3 chords. Note that this is different from my first example because there the 3 chords are all from the same major scale with the same root as the I chord (unlike in the blues, only the V chord could be a dominant seventh chord, not the others). In the blues, the chord scale for each of the 3 chords is the mixolydian scale with the respective roots. Nevertheless, it is important and helpful to realize that those 3 mixolydian scales share many common notes. The mixolydian scale of the IV chord is obtained by changing only one single note of the mixolydian scale of the I chord. The same is true for the mixolydian scale of the V chord.

It depends on the chord progression. If the chord progression implies a key change then you'd also change the key of your solo melody. In all other cases, you wouldn't change the key of your melody.

You gave a I-IV-V progression as an example. If you were to use the IV-major scale over the IV chord, you would make that chord sound like a new I chord, and not like the IV chord of the current key. The same is true for the V chord: by playing the V-major scale over it, it wouldn't sound like a dominant chord of the actual key; however, it is usually intended as a dominant chord leading back to the I chord.

Things are different if you have a modal piece like So What by Miles Davis. In the solo section you have D dorian (Dm7) before changing to Eb dorian (Ebm7). The Ebm7 chord does not function in the key of D minor, but it is something new. This means that in your solo you would change scales from D dorian to Eb dorian, simply reflecting what is happening harmonically.

Another different case is the blues. A basic I-IV-V blues is based on dominant seventh chords. There is no single chord scale for those 3 chords. Note that this is different from my first example because there the 3 chords are all from the same major scale with the same root as the I chord (unlike in the blues, only the V chord could be a dominant seventh chord, not the others). In the blues, the chord scale for each of the 3 chords is the mixolydian scale with the respective roots. Nevertheless, it is important and helpful to realize that those 3 mixolydian scales share many common notes. The mixolydian scale of the IV chord is obtained by changing only one single note of the mixolydian scale of the I chord. The same is true for the mixolydian scale of the V chord.

In sum, on order to be able to choose appropriate scales, you need to understand the harmony and the implied key (and, possibly, key changes) of the underlying progression, and you want to reflect all this in your solo. If your solo does not reflect the harmonic function of the current chord (if there is any) then the result will not be very musical.