Would you recommend stitching incisions up straight away after liposuction?

I disagree with most the other doctors I think most incisions need to stay open and I think especially for aggressive or HD liposuction you need certain areas of drains.
You need a formal evaluation by an expert in body shaping and contouring to determine what is best.  Traditional liposuction awake and smart liposuction are old methods and do very poorly for tightening skin or significant skin tightening or contouring.  Small problem areas can be improved slightly by these methods.  The best in body contouring not only removes fat with energy devices like VASER ultrasound but also internally heat the skin with radio-frequency devices such as J PLASMA/RENUVION, InMode BodyTite, ThermiRF to heat the under surface of the skin and tighten it at the same time as fat removal. These combinations are called 4D HIDEF VASER contouring and can only be done by a well . trained body contouring specialist. At the same time fat should be harvested, PRP and stem cells added and injected into muscles or indentations/cellulite to get body shaping and contouring.  This is known as a Brazilian butt lift when you inject the fat to the buttock for contouring and lifting, but fat can also be used in areas such as the chest/breast, arms/shoulders, calves and face.  Cellulite should also be treated with cellfina, sculptra, subcision and/or fillers such as bellafill, renuva synthetic fat, or sculptra.  If skin is very loose before surgery then it will need to be removed such as lower abdominal skin (tummy tuck/abdominoplasty), breast skin (breast lift), arm skin (brachioplasty).  Overall you need a full assessment, but simple liposuction alone will not tighten skin and needs a combination of various methods -- fat removal, skin tightening, defining, fat grafting, skin removal -- to get the best in body contouring and body sculpting.  Dr. Emer.

Dear Eleanoradoll,
a lot of plastic surgeons don't use drains for liposuction surgery and close their incisions so this is not unusual. Finding the right Dr. is extremely challenging especially with the number of online platforms and resources available. There a lot of great Dr's available. Definitely check to make sure your choice specializes in the procedure you want and spend the time to read through patient testimonials. 
You can always pick up the phone and call around also, find an office you feel comfortable with and set up a few consultations. 
Daniel Barrett, MD