I don't really see the point in all this. The only benefit I can see of this is a more visually appealing look, which is subjective and effects what is a relatively small amount of infrastructure in comparison to say the road network. OHLE is barely even noticeable when you factor in the signalling, ballast, rails, overgrowth and the fact many trains run through cuttings. Personally, I think it is visually appealing as it gives the impression of modern infrastructure.
Battery technology is expensive, heavy, creates losses and is already near it's limit of capacity. Perhaps on more rural and less well travelled routes, short sections of charging for battery powered trains could work as a great stop-gap for full electrification. There is no benefit, beyond potentially bringing electric traction to non-electrified routes or branches, to using battery powered trains where existing OHLE has existed.
3rd rail has already been proven outdated and until we supposedly leave the EU, we are unable to build new or replace existing OHLE with 3rd rail technology. The risk of electric shock means voltages higher than 1500v cannot be used, leading to higher transmission losses, and the need for more frequent feed points. (Which will negatively impact the appearance.) Due to these lower voltages, less power can be transmitted through the lines and therefore there is a limit to how many trains can be run. In fact, there has been talk of replacing the existing 3rd rail systems with OHLE. Due to the power issues and physical limitations of the shoes this makes it unsuitable for high speed running.
In regards to hydrogen trains, they suffer from many of the pitfalls of battery technology. Increased weight, cost and losses.
When it comes to reliability issues, these are already being solved by some newer trains. I stand to be corrected, but I believe the new LNER Azumas are fitted with one diesel engine per train, allowing a crawl capability in the case there is a loss of power. I think this is the best solution to the reliability issue, as it allows trains to move out or even through a broken section of OHLE, allowing services to keep running.
I think that infrastructure spending could be spent in a much more constructive way than ridding ourselves of the best traction method for trains to date. Our roads are full of potholes, large concrete road bridges cut through cities and traffic jams clog up streets. (Traffic could be improved by an increase in rail users

There are many concrete hangovers of the 60's covered in flammable cladding which is yet to be removed and parks/government buildings falling apart after years of neglect. I'm sure there are also many stations and buildings on the network which would benefit from some TLC and would bring a visual and service improvement to many more people than those who spend their time staring at sections of OHLE...