For many players, the fact that the iron frame supported instrument can easily sustain notes- with only fingers- is enough. Since the pieces originally would have been for clavichord or harpsichord: their sustain was very limited, so very often, pieces could only make more use of smaller notes rather than longer ones.
The pedals didn't exist back then
The main argument is those who are against using the pedal are for historical reasons: 'the pedals didn't exist back then'. Those who argue for the pedal to be used could say: 'we have to adapt to a modern piano'. Both points are valid- but can also be disproved.
After the first gravicembalo col piano e forte was built by Cristofori in 1709, the use of hammers with deer leather with larger strings and soundboards were developed. Thanks to further modifications by Silbermann and Zumpe, the early pianoforte grew in sonority and expanded quickly throughout Europe.
Originally the dampers came in the form of hand stops (similar to the idea for the organ). This became impractical to use the hands, so a knee lever came about in Germany in about 1765. These devices sustained the sound in a more selective way, such as sustaining either treble or bass. Beyer, in London, in 1777, introduced a pedal having a cleft foot to help with selective dampers. Throughout the 1780s, Broadwood, London and Erard in Paris developed the use of the pedal further.
By 1825, Alpheus Babcock invented the iron frame making a greater sustaining tone possible.
Taking J.S Bach as an example. Bach's years had spanned from 1685 to 1750. Through most of these years, we can see clearly the possibility of using sustain in pieces had existed in his lifetime.
The sustain was, however, weaker yet could sustain selected notes. We can compare this to the middle (sostenuto) pedal we use in modern pianos today. However, these did not come around until the 1840s by Boisselot and Sons in Marseille.
As far as the left 'una corda' pedal goes, the muted effect of playing only one string was introduced by Cristofori in 1726. The use of this effect had become more prominent by the 18th and 19th centuries, very well heard of by composers such as Beethoven.
With the existence of sustain capability and the ability to alter the tone. Why was this treated completely separate from Bach's style? We know of the great sustaining power an organ can create with its many stops of changing the sound. Bach was aware of this, being an organist himself.
If we argue that we cannot use the pedal as it 'didn't exist, then we could further the argument to say Bach's music shouldn't be played on the piano.
We have historical proof to say the idea of sustain did exist. It is true that the overall Baroque style did aim for clarity of contrapuntal parts- particularly on keyboards and orchestral music. Using sustain with the right pedal would cause loss of this clarity where it is important.
In Bach's time, creating a seamless legato on keyboards and organ was solely dependent on the fingers. Nevertheless, there was a pedal keyboard that could be attached to the clavichord or harpsichord. The strings could be played with the pedals as well as the hands. It was also used by organ students to practice. It couldn't be heard well from a distance, so it was ideal to avoid disturbing other people outside. This was nicknamed the 'dumb spinet'. This was the closest to using our modern middle pedal in the Baroque period. Bach had also owned one of these himself.
Pianist Busoni in his transcriptions of Bach's work, clarifies this also:
' do not believe in the legendary tradition, that Bach must be played without pedal… True, in the piano works, the inaudible use of the pedal is the only proper one. By this, we mean...binding two successive single tones or chords, for emphasising a suspension, for sustaining single parts etc.'
Busoni recommends that for repeated notes or arpeggiated chords, briefly use the right pedal to connect them. Although sustain can be used, it must be used sparingly, also, for a specific reason: such as to avoid a large gap in sound when the hand has to move a longer distance to the next note.
For the more organ style transcriptions, Busoni encourages much more pedalling as it provides the best imitation for 'full organ'. The una corda pedal could also be used not only for a quiet dynamic but for a 'peculiar effect' of a different colour.
Quite often, we also come across long pedal notes in Bach's works. They can last impossibly too long for the original instruments. We can be sympathetic to this by sustaining these notes with the middle pedal. In doing so, the clarity of the melodic parts remains unaffected. It is clear that for a note to be so long: the composer has at least some intention for this to happen.