The answer is no. Statistics show that new types have lower accident rates than older types.
Airbus has grouped aircraft into 4 categories: early jets, autopilot jets, glass cockpits, and FBW jets. They state
The lowest sustained fatal accident rate of first generation jets was around 3.0 accidents per million flights, whilst for the second generation it was around 0.7, meaning a reduction of fatal accidents of almost 80% between generations. In comparison, third generation jets now achieve about 0.2 accidents per million flights, a reduction of around a further 70%.
Finally, fourth generation jets have the lowest accident rate of all, at a stable average rate of about 0.1 fatal accidents per million flights, which
is a further 50% reduction compared to the third generation.
They provide charts (page 17) which show that the accident rate of FBW planes is half that of third-gen glass cockpit planes over the last 10 years.
New aircraft have features like auto-TCAS, auto depressurization descent, and landing distance monitoring, that aren't available on older models. These enhance safety.
Certainly certification and crashworthiness standards have improved over time. For example, 16 G crashworthy seats were introduced in 1988. Improved access to exits and fire resistant materials were other requirements phased in by the FAA.
And finally, the FAA now has the position that you cannot maintain an aircraft safely forever, with regulations called the Limits of Validity. As an aircraft ages, the structure incurs fatigue damage. At one point, the damage will be so prevalent, that cracks will merge and you'll have an Aloha 737 accident.
Concerns that such damage will be missed or occur in areas that cannot be inspected have led to the LOV, which is an upper flight cycle/flight hour limit at which the aircraft must be scrapped. Notably, this was something that Soviet/CIS certified aircraft always had.