Could new satellites be designed to intercept other older functioning artificial satellites or space junk already in orbit to add weight to the new satellite in order to last longer in orbit?
There have been projects with this intention, such as OLEV, but actually, this would only allow increasing the life of a satellite from a propellant and orbit maintenance point of view.
Theoretically it is possible, but one would expect other systems in the satellite to fail, particularly the battery would loose maximum charge and panels would loose efficiency over time. You could send an appendix satellite with a new battery to the old spacecraft, but at some point, you are very likely to have enough failures in non-standard devices such as the payload that would are better of launching a new satellite.
Also, there are several projects and discussions about space thugs, which would be able to capture and get rid of space debris. An alledgedly first case would be the RemoveDEBRIS satellite. But in this case, the end goal is to de-orbit a defunct satellite or random debris, instead of amking it last longer in orbit.
Hence, the current practice answers your question with "no, it wouldn't be better", as far a "better" could be understood as whatever governments and the free market have decided to do so far.
Note as well that due to technology improvement, it is unlikely that repairing spacecrafts in orbit will ever be a thing. For instance, while geostationary satellites are designed to last for 15 years, their throughput has been increasing very fast in the few last years, to the point where "The first two ViaSat-3 satellites are expected to deliver more than twice the total network capacity of the approximately 400 commercial communications satellites in space today – combined.". Hence why performing costly repairs on old, low-capacity satellites that are loosing reliability instead of launching new, modern ones?