In my considered opinion, as somebody with two engineering degrees and a CPL: "it depends".
If you want to be a commissioned military pilot, test pilot, or seek a future combined flying / engineering role - go for it.
If you want to be an aeronautical engineer with a grasp of flying to support your work - do a PPL; maybe upgrade to a CPL later when you have time and money, and reasons to have it. (Although CPL theory is actually quite useful as an aeronautical engineer).
If you happen to have a fascination for engineering and would like to study it anyhow - what the heck - go for it.
If you "only" want to be a professional pilot:airline, instructor, NCO military - no desire to take a technical role, be a military officer, etc - stick to the CPL and don't waste several years and tens of thousands of dollars on an education you won't enjoy and won't use.
That said some countries do need some kind of degree for airline pilots just as a condition of employment. In that case do the minimum you need, and something you'll enjoy. But Aero Eng is an incredibly demanding subject so you need to have a passion for it. If you don't, do something you do enjoy - or maybe something like management which may be of value to you as you climb the professional career ladder.
If you want a backup in case you lose your medical, do something you can earn money with quickly. That's not usually an engineering degree, which is very much a licence to learn requiring several years more professional experience to be much use to anybody. A cookery, teaching, technician qualification would be more valuable in that context.