Pilot reported a near CFIT incident with a tower while being vectored for traffic on flight following.

Narrative

I called San Antonio Approach for flight following about 20 miles north of the SAT VOR with destination Castroville (CVB; which is SW of SAT). After the second vector for traffic on a heading of 250 degrees with instructions to remain at or below 3500 ft.; the Controller hands me off to the next Controller while I am still pointed at a 3049 ft. tower (I was 3000 ft. staying below overcast with 4 mile vis.). The next Controller was busy giving continuous vectors to other aircraft. When I finally got through to check in; I just canceled VFR flight following and turned away from the tower at my 12 o'clock; 3 miles (1 minute at my airspeed). I believe a simple descent would have addressed the traffic conflict without this last vector. I also believe the Controller could have cleared me direct destination before he handed me off to avoid a potential CFIT. I fly into San Antonio a lot; and the Controllers are usually top notch; but this surely violates SOPs and discourages VFR pilots from getting flight following; which negatively impacts safety. Had I not been familiar with the area including the tall towers; it could have ended tragically. On the same day (8 hours later) I called the TRACON and discussed the situation with the Controller on duty (different Controller). He was very friendly; took the information; and said they would be back in touch after reviewing the tapes.