The most budget way is to self-drive. For example, Marriott points for the Protea Kruger Gate hotel and drive yourself around pay for guided drives (either full day with a private guide or evening / night drives with SANParks vehicles from the gate). There are restrictions to being in a National Park, but also the ability to travel long distances to see more variety and wildlife density is very high.

There are package holiday deals from the UK that can be part-paid with frequent flyer miles but they tend to be poor value for points. Or just accommodation booked as hotels with points. But in the sense of "Are there any reasons I should avoid booking a safari with miles/points"? Safari lodges tend to be independent or in multi-national operator groups. I would imagine the high-end safari operators wouldn't want their reputation or image affcted by seemingly offering something for free. So you tend to see hotels or lodges that have spare capacity offering rooms for points - they may be getting a poor rate but want full capacity - so the big lodges that suit tour travel or lodges in locations that aren't at the highest premium. For example, you can get very good accommodation in places like Pilanesburg NP with moderately good wildlife viewing, it's just a relatively small Park. Around the Kruger area in South Africa, most of the lodges you see that offer safaris are in fenced private reserves, so are stocked and managed. Having looked at e.g. British Airways Avios, you can book a few lodges in the greater Kruger (unfenced from the National Park) in Balule reserve and the points value is moderate - not as good as booking premium cabin redemption flights but not awful. I think the biggest reason to avoid booking lodges with points is the effective lack of flexibility - there are thousands of options and given the time and money you'll be spending it seems a shame to not choose the best option for your likes and requirements.