Firstly, assure that the airspace you're in welcomes you at higher altitudes, it gets more and more controlled up there. Also, consider the requirements for having oxygen available above 10,000 feet. Consider your, and your passenger's health in terms of breathing thin air.
Yes, as you fly higher, your speed may increase due to less dense air, but then in a 152, your power decreases, so the net effect is poor, and easily overcome by small unfavourable winds.
The service ceiling of the plane is affected by many factors, but, you may have found it that day, for that plane, with that load. I have tested a few planes to their absolute ceiling for engine certification testing. Personal record: 20,800 feet in a normally aspirated Cessna 185 configured with a carburetor, running on auto gas (we were testing for vapour lock and fuel flow at high altitude on the auto gas). Manifold pressure at full open throttle was 12", stall horn on, 72 MIAS. I had the plane just over 21,000 feet, but it would not stay up there under power. Oxygen was obviously used. Personal record in a C 150, two up, and carrying traveling kit in the back was 13,200 feet, which we reached at greatly reduced power, being carried aloft on a sever mountain wave over the Appalachian Mountains in the US. We were quite afraid that we might be carried higher, as we had no intention to be that high, and had no oxygen! Later in the flight we encountered settling air, and were taken back down a few thousand feet.
Correct, you'll get to the point where at full power, you're flying just above stall speed, and not climbing - that's it. Note that in part, the normally aspirated C 152 engine will be developing pitiful power up there. Also be aware that it may begin to run rough in thinner air, if the mag leads aren't in tip top condition. It's not a problem, as the problem will resolve itself as you descend - though if you're going to go high regularly, have new mag leads installed. Cracked insulation in old leads allows the spark to go to ground on the shield before it gets to the plug. Thinner air allows sparks to travel more easily.
Unless you have immensely favourable winds way up high, there's otherwise not much reason to go way up. The fuel burned getting up there, and slower climb, won't generally be recovered in added cruise speed. Consult the POH performance charts, and the winds aloft, an go only as high as you need to. If you're crossing a body of water, or other un landable terrain, higher may be better, if all other things are equal.