Yes! You should go through the effort to secure restitution for such a significant valuable resource.
There is a perfectly objective valuation formula quite often used by certified arborists: the International Society of Arboriculture has generated
The Guide for Plant Appraisal, 10th Edition. The appraisal system is the standard for determining a tree's value for insurance or lawsuit purposes, and withstands testing in the court system. It is not necessary - but additionally helpful - if trees are additionally protected by law/statute in your area.
https://www.isa-arbor.com/News....
I work for local government in Kentucky, and the local parks department has valued and successfully secured restitution many times through claims with automobile insurance companies and even with local utility companies which damaged or unnecessarily removed trees. Your tree may be worth upwards of $50,000 - depending on a variety of factors including health/condition, species (
Quercus sp.), size (50 feet tall, circumference, etc.), and location. More people today are expounding on the environmental and ecological services that such mature trees provide - which you and your neighborhood have now been deprived of. These include stormwater management (big old trees have a tree-mendous amount of surface area to get wet, and they absorb and use groundwater through their roots); habitat for many birds/mammals; food source for many insects/birds/mammals; and environmental mitigation for heat/sunlight (shade) which translates to energy saving for homes, and deflection/reduction in wind effects. There are likely many more items that could be listed in this regard, but are harder to quantify for compensation - such as history, nostalgia, and beauty.
If you have documentation - recent photographs of the tree, receipts from work done by licensed professional arborists, or testimony from same - that will make it far more likely to demonstrate the loss and win such a case. You should also seek the counsel of such a professional arborist (and/or attorney) for similar cases and the proper approach to be successful.
Minimally, one should document the loss - and impress upon all that will listen what big old trees are worth, and that their loss should NEVER be taken lightly. Become (and train up) a community advocate for trees, and always argue against unnecessary, ill-considered, or casual removals simply because the trees have no (audible) voice.