Note: This answer was only intended to answer the question focusing on Masato Suzuki's own remark. His remark may or may not be applicable to the general opinion (see also the comment thread).
There was another interview in Japanese with Masato Suzuki on Toppan Hall, touching on the topic of playing Bach's works with harpsichord and piano.
Relevant quotation:
―― 最初に弾いたのはいつですか?
鈴木: [...]。ピアノのレッスンで平均律を習ったときは、家でチェンバロで弾くのと、先生のところでピアノで弾くのとで、葛藤していた時期があったな…。ピアノではどうも、うまく弾けなくて。
―― どういうところがですか?
鈴木: 父がチェンバロで弾くのをずっと聴いていたし、僕自身もチェンバロで一番弾いていて。チェンバロのやり方に慣れていたので、まったく別のアプローチで弾かなければならないことに違和感があったんです。ピアノで弾いてもいい曲には変わりないですし、いまもピアノで弾くことはあります。でもチェンバロという楽器の良さである、音が即興的につながっていく感覚や、フーガみたいに高度な情報処理が必要な曲では、やっぱりチェンバロのために書かれた作品なんだと実感するんですよね。
―― ピアノで弾くと、どういうところが引っかかるのでしょう。
鈴木: ピアノは打鍵によって一音一音、音量の違いがつくれるので、ある声部を際立たせたり、沈ませたりということができますが、そこが逆に障害になるんです。チェンバロはそれができないので、必然的に全部の声部を平等に歌うことになる。すべてをくっきりアーティキュレーションすればするほど、フーガとして立体的になっていきます。そもそもチェンバロは通奏低音を担う即興的な楽器で、当時はソロを弾くほうが例外。バッハも通奏低音としての可能性を追求していただろうし。面白いのは、バッハの譜面は完璧なんですけど、弾き手に想像の余地を残している。たとえば、あるテーマでフーガを即興しようとしたときに、良いものになるよう磨けば磨くほど、彼の譜面に近づいていくような感覚があります。即興演奏のひとつのモデルケースとして、楽譜があるような。書かれている通りに完璧に演奏することも大事ですが、そこには必ず即興的要素がある。だから、チェンバロで弾くと納得がいくのかもしれません。楽譜のリアリゼーションとしては、ピアノでもオルガンでも、アコーディオンだって可能なんですけどね。バッハをピアノで聴いたときに、すごく好きだと感じることは少ないです。むしろ趣味で、ピアノで弾くバッハは楽しいですけど(笑)。
Translated (with the assistance of DeepL, manually reviewed):
―― When did you first play it?
Suzuki: [...]. When I learned the Well-Tempered Clavier1 in piano lessons, there was a time when I was conflicted between playing on the harpsichord at home and playing on the piano at the teacher's place... I couldn't play well on the piano.
―― What do you mean by that?
Suzuki: I had always listened to my father play on the harpsichord, and I myself played the harpsichord the most. I was used to the harpsichord method, so I felt uncomfortable with having to play it in a completely different approach. It is still a good piece to play on the piano, and even now I sometimes play it on the piano. However, the harpsichord has its own advantages, such as the sense of improvisational connection of sounds, and in pieces that require advanced information processing, such as a fugue, I feel that the piece was written for the harpsichord.
―― What aspects does it bother you when played on the piano?
Suzuki: The piano can create a difference in volume with each note by hitting a key, so it is possible to make a certain part of the voice stand out or be subdued, but this also makes a hindrance to the piano. The harpsichord cannot do this, so it is inevitable that all parts of the voice are played equally. The more clearly articulated all the voices are, the more three-dimensional the fugue becomes. In the first place, the harpsichord is an improvisational instrument that serves as a bass continuo, and at that time it was more the exception than the rule to play solo. And Bach would have pursued its potential as a figured bass. What is interesting is that even though Bach's score is perfect, he leaves room for the player's imagination. For example, when I try to improvise a fugue on a certain theme, the more I polish it to make it good, the closer I get to his score. It's like the score is one model case of improvisation. While it is important to play perfectly as written, there is always an element of improvisation. Maybe that is why playing on the harpsichord is so satisfying. As for realizing the score, it is possible on piano, organ, or even accordion. When I hear Bach on the piano, I rarely feel that I like it very much. Rather, as a hobby, I enjoy playing Bach on the piano (laughs).
1 Thanks Brian Chandler for the correction!