Losartan itself has a very short half life, but it's usefully extended by an active metabolite. Still its window of effect is significantly shorter than azilsartan or telmisartan. Of those two, telmisartan has the longer half life but azilsaran has a longer binding to AT1R. I've used both and there is little actual difference in practice. Being a cheap generic, I do not see why any doctor would prefer Losartan over telmisartan; azilsartan is still brand name (Edarbi) in USA maybe for another year or so. I suppose you could request telmisartan prescription for its added benefits via PPARγ/⍺ activation? Not that your PCP probably has any idea what that is...
If I were you, I'd just escape your PCP and buy Cilnep-T from PCT24x7 and use that. You'll get the superior ARB and cilnidipine is superior to amlodipine in every possible way (and getting a TelyRx prescription for that is not possible since it is not a formulary drug in USA). If your potassium runs on the higher side with an ARB or you want a little extra BP control, get the Telmiheal Trio which is a 3-in-1 combo pill that has telmisartan 40mg, cilnidipine 10mg, and chlorthalidone 6.25mg.
If you go with Cilnep-T, you can still get a TelyRx prescription for Indapamide or chlorthalidone as an add-on if needed/wanted; they're similar but indapamide is more potent and available in lower dosages 2.5mg versus 25mg for chlorthalidone.
I've been using either (Cilnep-T + Telmiheal Trio one ea per day), or (2) Cilnep-T + one 2.5mg indapamide per day) and the combo of ARB, CCB, and thiazide-like diuretic keep my BP perfect - even on 500mg anabolics and 7.5iu GH. Generally it stays in the 110-65 - 120/75 range.
The low cost Cilnidipine 10 or 20mg is made by the same company as the Telmiheal Trio (Healing Pharma)... so far I've been very satisfied with their medications. Have several others from them too including quetiapine (one quarter tab = 6.25mg for sleep) and they all work great and are nicely pressed and the blister packs are air tight.
I was diagnosed with diastolic HTN when natural and prescribed Edarbi by a cardiologist - it was $50/mo via manufacturer program as my insurance did not cover it. And I now see why because telmisartan is basically just as good (potentially better in some ways) and already a cheap generic.