I did T3 and T4 back in my Fitness modeling days. I first did periods of T4, later switched to T3. Here´s my experience, which I experienced myself, and what role T3 and T4 play in sports:
First, even when used on healthy people, it´s not doping. Neither Liothyronine (T3) nor Levothyroxine (T4) are on the list of WADA´s banned substances.
I did cycles of T4 up to 400 mcg a day, for 4-8 weeks. Later cycles included up to 100 mcg of T3 for also 4-8 weeks. This hormones are, in these dosages, for cutting purposes. It increases metabolism drastically. With 100 mcgs of T3 a day, after some time (it takes few days to work), one has a metabolism that you could sit on the couch 24h a day, and still burn 3000-4000 calories a day, while not being on T3, this would need maybe 1300-1400 calories a day.
T4 has weaker effects, it´s 3-5 times weaker than T3. T4 has to be transformed into T3 by the body, to work. Only T3 works directly. If you create an extremely high T4 level, the body will stop transforming this into T3, so the T3 levels don´t grow equally, so the benefits won´t come any more, after some time.
It´s useless to take only T4, I today would say.
Then, don´t forget we speak about hormones. If you take 600mgs of caffeine, they´ve left the body after hours. It´s not super healthy for heart, liver and kidneys if you do this 4 times a week or daily, but it´s rather harmless. If you don´t do that for 20 years, the long-term consequences are acceptable, not very high at all.
Taking hormones (T3, T4, EPO, testosterone, HGH) is a different story. These are all substances the body also produces endogenous. If you start to add exogenous hormone, the body ALWAYS tries to balane this out, and will decrease or stop producing own hormone. The longer and higher dosed you add exogenous hormone, the more drastic this decrease will be.
There a different ways athletes try to recover their endogenous production after periods of use of hormones.
EPO: no post-cycle therapy
Steroids/Testosterone: HCG, Clomiphene, antiestrogens in general
HGH: no post-cycle therapy
T3/T4: slow lowering of daily dose, over 1-2 weeks
I, for myself, need T3/T4 now also for medical reasons. My endogenous production hasn´t recovered properly, I (like many other athletes) created a life-long hypothyreodism, which needs to be treated by life-long (now, of course, lower dosed) T3 and T4 medication, every morning, half an hour before breakfast. I knew the risks, and knew the damage it could do to my health, I accepted it, and so now, I don´t regret anything.
I have to say T3 and T4 get lower dosed in endurance sports, so this damage might be smaller. However, also with lower dose, there isn´t any guarantee that your thyroid system will recover afterwards.
Levothyroxine and especially Liothyronin are extremly powerful hormones, and Liothyronin´s effect on metabolism is almost unique (only DNP is stronger). Lower dose of T3 are less metabolism-increasing, but even slightly anabolic.
The side effects of T3/T4 however (= the side effects of hyperthyreodism), aren´t funny. Also, the effects of the hypothyreodism you maybe will face afterwards, aren´t funny (low metabolism, weakness, freezing also at 30 degree Celsius, ...).
I´ve never taken EPO, but after these thyroid experiences, I suppose someone who used EPO years and in high doses, creates anemia.