There’s an argument on the relative value of Peshat and Derash rolling in a comment thread on the Seforim blog. One commenter has taken a position that
a) Drush is the by far more important, and probably the only correct, form of biblical interpretation.
b) Certain unnamed “Modern Orthodox” scholars, by engaging in “pshat” style interpretation, are, by doing so, demonstrating their favor of the Documentary Hypothesis. By implication, they oppose Orthodox Judaism, which takes the accurate transmission of the Biblical text from Sinai as an underlying truth of its system.
I don't think any of the Orthodox rabbis and other personae (Dr. Nechama Leibowitz, and even her brother, Dr. Isaiah Leibowitz) reject the drashot that engender/support Torah sheb'al Peh (Oral Torah). In fact, as Orthodox personae, by definition they can't reject such interpretive models, because how else do Chazal (our Sages of blessed memory) link the Torah text to the halacha given at Sinai, and the halacha practiced today?
Chazal's interpretive mode was drush (exegesis following hermeneutical rules) - their interpretive works are the Midrashim, even down to the Zohar, which is ultimately a halachic midrash, even if a late one in final redaction - a midrashic-style work with the authority of a Rishon. (high-medieval sage)
But halacha as engendered by drush from pesukim (verses) does not happen any more. The authorized drashot are already authorized, there really can't be any more. So what else is there left open to modern exegetes, but pshat? Maybe one can come up with drashot, which support the predetermined conclusions of Chazal, but they will generally be rejected. Pshat, however, is almost by definition not legally binding, while still bringing out subtleties in the God-given text.
One can always make diyukim (points based on grammatical or morphological subtleties) on mishnayot or gemaras, and find more details of halacha that way, but doing so on verses is not kosher any more, unless it's just in support of existing halachic or ethical values. And that's where contemporary pshat (literal/literary) interpretation comes in.
Not everyone inclines to Talmud, but may have a head that likes to engage in Torah interpretation. For instance, my cousin Dr. Ed Greenstein, wanted to devote his life to Torah, but was not particularly interested in Talmud, so he got a PhD in Bible.
The Rishonim led the way by beginning the enterprise of pshat-style interpretation, finding the literary level of the Torah text as opposed to the legal level. Both should ideally lead to an ethical lesson. Even the so-called "fault-finding school" looks to the Avos for lessons in life; even if they find apparent faults in the lives of the Avos, the way they or we overcame them, gives us chizuk to overcome our own faults, particularly at this time of year.
In the time of the Rishonim, there was still some reliable Oral Torah tradition from Sinai, so drush was still a useful mode of interpretation for creating halachic lessons. Today, we don't really have anything authoritatively from Sinai that has not yet been written down, so what is left for us, but to approach the text on its own terms, and see what lessons it has to bring itself?
Not every commentator, even in history, had equal strengths in Talmud and Bible. So too today. Don't write off the entire enterprise of contemporary Biblical interpretation because you choose to dismiss "ein mikra yotzei miydei peshuto". It still holds (except where the literal level is totally unbelievable; see Meiri in Avos on "megaleh panim shelo kehalacha"); it may not be the level of interpretation that generates halachoth - that's the interpretation of the 13 Middoth, the Midrashim, the Talmud, but it is still a valid, and valued, approach to the text.