I'm going to differ from the crowd and say replace the unmaintained 10y/o water heater before it leaks, especially if there is a remote possibility of water damage. Regardless of how long a well-maintained WH can last, you are at the end of life for your unmaintained WH.
How I know:
My house had a 9 y/o WH (with 9y warranty) in a bathroom closet when I bought it, and no drain pan underneath. I vowed to replace it before it leaked all over the floor, but never got around to it due to other projects. Two years later, it leaked. The water went under the bathroom tile, soaking what I later discovered to be particle board. The bathroom was taken down to the subfloor, and we ended up taking the walls to the studs too. We went about 3 weeks without hot water in December 2021 as I did emergency mold remediation and relocated the plumbing and new WH to an outdoor closet. Plumbers have long wait times in December, so this was as fast as the situation could be remedied.
This is why factories replace equipment before the equipment fails, and presumably while the equipment might - or might not - have plenty of life remaining. The disruption to other activities is just not worth it.
The tradeoff is this: Potentially getting another year or two worth of value out of the old WH versus experiencing the kind of chaos I experienced. I would have paid maybe $100 to have avoided being unable to shower, wash hands properly, etc. in my own home (DW might have paid $250) and as you can see we're well over the value of any remaining lifespan in a 10y/o WH. Also, what's the use of putting a $50 anode in a WH that is probably already rusted out? Just start fresh.
Also consider that WH's are going up in price due to inflation, just like everything else. At 5% inflation, your new $700 WH gets $35 more expensive each year you squeeze out of the old one. Thus, much of what you have to gain from getting one more year out of your old WH gets spent on inflation, at least in the short term. I.e. if a $700 WH lasts 10 years, it depreciates $70/year. But you don't get to enjoy the benefit of $70 in free depreciation because you'll pay $35 more to replace the WH for each year you get past the unit's lifespan. So you're actually chasing $35 in value at the risk of having your whole lifestyle put on hold at an inconvenient time.
WRT replacing anodes, I've never done it either, but plan to when my new WH reaches about 5 years old. You do not need massive overhead clearance to get the old anode out - it can just bend on its way out. Replacement anodes are built like a chain so they can drop into the hole with minimal overhead space. Good question on how to secure the WH while cranking a pipe wrench or socket. I might just whack the wrench/ratchet with a hammer while the tank is full (but valve is off) instead of pushing it.
