The reactors you mention used what would today be considered obsolete technology (like virtually all of the reactors in use today.) It is possible to create a reactor which will not "melt down as they did. However, all complex systems are prone to failure. So, power outages (both planned and unplanned) will occur. Meltdowns should not.
One of the things which concerns me is the fact that almost all nuclear reactors in use today would be called Generation II Reactors, designed to be used for years even decades less than their current life-spans. In my opinion, those old reactors should be shut down, but we must not replace them with fossil fuel, and renewable energy has significant challenges.
In 2022, the National Renewable Energy Laboratory produced a study, Examining Supply-Side Options To Achieve 100% Clean Electricity by 2035. The scenarios they look at include maintaining or increasing current levels of nuclear generation (remember, these people have been studying renewable energy since Gerald Ford was president.) I highly recommend the study to anybody who is not locked into a dogmatic position (either No Nukes or No Renewables.)
The key is, we need to dramatically cut emissions almost immediately (we should have done it decades ago.)
Proposed new fission reactors are generally classified as Generation IV Reactors. (There were few Generation III Reactors built.) There are a number of different proposed Gen IV reactor designs. Really, Gen IV, means a newer design than Gen III. Although there are a number of plans, they must go through a lengthy review process. (The lessons of the meltdowns you cite are not lost on government regulators.)
Personally, I prefer nuclear fusion. Fusion reactors (by nature) will be extremely safe. Its difficult to get fusion going, and keep it going, and (with one notable exception) it currently takes more energy to fuse atoms than the reaction produces. Timelines call for practical nuclear fusion in as few as 5 years, and the approval process will be much faster than for nuclear fission reactors. (Deploying hundreds of new reactors, whether fusion or fission will take several years.)
Wind (and increasingly) solar are relatively inexpensive, and relatively quickly deployed. Their challenges are not insurmountable, however, a 100% renewable grid just isnt in the cards at this time.