I don't know what you're reading but it clearly states unsubsidized wind in the second graph (which has the same value as the first graph).
Regarding subsididies while it does not receive the most subsidies now nuclear has received 66% of the R&D and demonstration subsidies from 1974-2007 in the EU. It still receives about half of what solar receives [1]. So despite it having received much more subsidies previously its still not viable.
I'm sorry, I have misread your source. It clearly states "unsubsidized". My bad.
I think my points about the LCOE still stand, though. The LCOE is not a good measurement for comparing intermittent and baseload power sources. Nuclear in particular suffers here since the capital costs are very high compared to operating costs. A nuclear power plant needs to run close to maximum power all the time for maximum profitability. This artifically inflates the numbers for nuclear while lowering the apparent cost for intermittent sources.
Regarding your second paragraph, I'm not sure if you're arguing that the EU spends half the amount on nuclear power R&D as solar power R&D, or if you're talking about subsidies for the plants themselves. I'd argue grants for R&D projects would be very hard to count in a meaningful way, and I don't think e.g. a research grant that results in more efficient solar voltaic cells should count as a subsidy towards solar power, nor nuclear fission research as a subsidy towards nuclear power.
The EU provides grants for constructing e.g. wind power farms. Unfortunately, I'm not familiar with every country, but in Sweden, renewables are given a large cashback grant per kWh generated ("elcertifikat"). Nuclear power here has been profitable since the 70s, and didn't turn unprofitable until taxes on nuclear power were increased substantially a few years ago.
Regarding subsididies while it does not receive the most subsidies now nuclear has received 66% of the R&D and demonstration subsidies from 1974-2007 in the EU. It still receives about half of what solar receives [1]. So despite it having received much more subsidies previously its still not viable.
[1] https://en.m.wikipedia.org/wiki/Energy_subsidy