Opening a Muhaadarah with the recitation of some verses of the Quran is permissible as long as it is not taken as a sunnah or a common habit, especially if the verses being recited relate to the situation.

Ash-Shaykh al-Uthaymeen, may Allah have mercy upon him, said:

لا ينبغي أن يجعل ابتداء الحفلات والندوات بالقرآن دائماً،

It is not appropriate to begin the celebrations and the seminars with the Quran

لكن لو كان هناك محاضرة وموضوع المحاضرة في الصيام مثلاً،
However if there is a lecture while the topic of the lecture is relating to fasting for example,

وأراد أحد أن يقرأ آيات الصيام في مقدمة المحاضرة هذا لا بأس به

And one intends to recite the verses pertaining to fasting at the beginning of the lecture, there is no harm in this,

؛ لأن المقصود هو أن نستمع للآيات التي في الصيام ثم نبني المحاضرة على هذه الآيات.
Because what is intended is that we listen to the verses regarding fasting. Then, we base the lecture upon those verses

ضمن لقاءات الباب المفتوح للشيخ ابن عثيمين رحمه الله

Ash-Shaykh Ahmad an-Najmi, may Allah have mercy upon him, said:

فأنا لا أعرف عن السلف مثل هذا الفعل

I am unaware of the likes of this act from the salaf

وإنما إذا فعلوه في بعض الأحيان إيثارا للمصلحة ولم يتخذوه سنة جارية فإن ذلك جائز فيما أرى

Rather if they done so at sometimes in giving preference to the benefit (and) they wouldn’t take it as a ongoing sunnah, (then) for verily that is permissible according to what I hold.

(Al-Fataawa al-Jaliyyah)

Ash-Shaykh Abdur-Razaaq al-Afeefy, may Allah have mercy upon him, said:

افتتاح المجالس رسميا بتلاوة القرآن حيث لم يرد فيه نص فلا يتخذ عادة ويجوز فعله احيانا

To officially open the gatherings with the recitation of the Quran, wherein there is no text for, is not to be taken as a habit and it is permissible to perform it sometimes.

(Fataawa of al-Afeefy)

Also this is the reason it was done sometimes at the gatherings of Shaykh Bin Baaz and not done always. However, some were lenient to make it a common habit. However, the correct opinion (is that) if it is taken as a habit it becomes an act of innovation.
And Allah knows best.

~ Abu Fajr AbdulFattaah bin Uthman